A Comprehensive Approach to Biodiesel Blend Selection Using GRA-TOPSIS: A Case Study of Waste Cooking Oils in Egypt

Abstract

The transition to sustainable energy sources is critical for addressing global environmental challenges. In 2017, Egypt produced about 500,000 tons of waste cooking oil from various sources including food industries, restaurants and hotels. Sadly, 90% of households choose to dispose of their used cooking oil by pouring it down the drain or into their village’s sewers instead of using proper disposal methods. The process involves converting waste cooking oil (WCO) into biodiesel.This study introduces a multi-criteria decision-making approach to identify the optimal biodiesel blend from waste cooking oils in Egypt. By leveraging the grey relational analysis (GRA) combined with the technique for order preference by similarity to the ideal solution (TOPSIS), we evaluate eight biodiesel blends (diesel, B5, B10, B20, B30, B50, B75, B100) against various performance metrics, including carbon monoxide, carbon dioxide, nitrogen oxides, hydrocarbons, particulate matter, engine power, fuel consumption, engine noise, and exhaust gas temperature. The experimental analysis used a single-cylinder, constant-speed, direct-injection eight cylinder diesel engine under varying load conditions. Our methodology involved feature engineering and model building to enhance predictive accuracy. The results demonstrated significant improvements in monitoring accuracy, with diesel, B5, and B20 emerging as the top-performing blends. Notably, the B5 blend showed the best overall performance, balancing efficiency and emissions. This study highlights the potential of integrating advanced AI-driven decision-making frameworks into biodiesel blend selection, promoting cleaner energy solutions and optimizing engine performance. Our findings underscore the substantial benefits of waste cooking oils for biodiesel production, contributing to environmental sustainability and energy efficiency.

1. Introduction

Energy is crucial for the development and research efforts of developing countries. However, the use of petroleum fuels leads to the release of gases that contribute to environmental pollution, acid rain, and global warming [1]. These emissions include carbon dioxide (CO₂), nitrogen oxides (NO_x), sulfur oxides (SO_x), and particulate matter (PM), all of which pose significant environmental and health challenges. CO₂ is a major greenhouse gas contributing to global warming, while NO_x and SO_x are precursors to acid rain, which damages ecosystems, buildings, and human health [2]. Additionally, particulate matter can penetrate deep into the respiratory system, causing serious health problems such as asthma, lung cancer, and cardiovascular diseases [3].

This poses significant challenges for all countries, particularly for developing nations that often lack the infrastructure and resources to mitigate these impacts. Fossil fuels, used in industry, agriculture, and transportation, are a vital energy source [2,4]. However, their availability is limited and diminishes annually due to increased consumption. This diminishing availability drives up costs and makes economies vulnerable to supply disruptions. Furthermore, the extraction, processing, and consumption of fossil fuels result in substantial environmental degradation, including deforestation, oil spills, and habitat destruction [5]. The reliance on fossil fuels also has socioeconomic implications, including health care costs due to pollution-related diseases and reduced productivity due to health impacts on workers [3].

To address these challenges, exploring sustainable alternatives to petroleum fuels is imperative. Clean energy sources such as wind and solar power have garnered significant attention due to their potential to support economic growth and mitigate environmental impacts. However, the intermittent nature of wind and solar energy, influenced by weather and geographic conditions, poses challenges for their short-term replacement of fossil fuels. Consequently, biofuels have emerged as a viable alternative, offering benefits such as clean combustion, low emissions, renewable and large-scale production availability, a non-toxic nature, safe storage, and compatibility with existing petroleum diesel infrastructure [6,7,8,9].

Biofuels can be produced from various sources, including vegetable oils, algae, animal fats, and waste cooking oils. Making biodiesel from new edible oils can impact food production and water consumption globally. For biodiesel production to be cost-effective compared to petroleum diesel, it should be derived from waste cooking oils. Producing biodiesel from used cooking oil is environmentally beneficial, as it offers several advantages from a waste management perspective. Providing a cleaner way to dispose of used oils results in reductions carbon dioxide levels. There are significant gains from reducing pollution resulting from car exhaust. Greenhouse gas emissions are reduced by 41% through the production and burning of biodiesel. There is a much better life cycle analysis when using biofuels produced from used oils [10].

In Egypt, over five million tons of edible oils are consumed in homes, fast-food restaurants, and food processing factories. Dietary habits in Egypt include the consumption of falafel (made from green bean paste), potatoes, and fish, all commonly fried in vegetable oil. These foods are popular in most households and in many restaurants throughout Egyptian cities and villages. There are millions of liters of used oil being disposed of in sewage networks, polluting waterways and increasing the costs of treating liquid waste [11,12]. Recently, some merchants have started collecting used oils from homes and restaurants to sell them after removing impurities. However, due to the lack of a law regulating the collection process, some of these oils are reused, making people sick with diseases. Because of the importance of this issue and the adverse effects of using fossil fuels on emissions and environmental pollution levels, many researchers have studied biodiesel production and its impact on reducing harmful emissions.

An estimated 500,000 tons of cooking oil waste is produced annually in Egypt. For 90% of households, finding a way to dispose of their used cooking oil (UCO) results in pouring it down the drain or into their village’s sewers rather than using a proper disposal technique. As this continues, drainage systems and crops suffer, further jeopardizing their vulnerable living conditions. This paper proposes the selection of an energy source from waste by introducing a new idea of turning used cooking oil into biodiesel—a green fuel that can be used in conventional diesel engines, directly substituting or extending the supplies of traditional petroleum diesel. The process involves filtering the oil and adding chemical additives until the final product, biodiesel, is obtained. The conversion process takes around three hours and produces two products: biodiesel and glycerin [13].

The proposed biodiesel production from waste cooking oil in Egypt aims to meet local fuel needs and adhere to international biofuel standards. This study leverages a grey relational analysis (GRA) combined with the technique for order preference by similarity to the ideal solution (TOPSIS) to evaluate various performance metrics of biodiesel blends. By integrating advanced AI-driven decision-making frameworks, this study highlights significant improvements in monitoring accuracy and environmental impacts. The research’s novelty lies in its comprehensive approach to biodiesel blend selection, promoting cleaner energy solutions and optimizing engine performance. The findings demonstrate that biodiesel, particularly the B5 blend, offers a balanced solution for efficiency and emissions, underscoring the potential of waste cooking oils in biodiesel production [14].

A pivotal study conducted in 2015 accentuates the strategic selection of microalgae strains for biodiesel production, underscoring the essence of sustainable biofuel production. Through the application of MCDA methodologies, including the analytic hierarchy process (AHP), weighted sum method (WSM), and others, this research pinpointed optimal microalgae strains for biodiesel production, showcasing the efficacy of MCDA in steering towards sustainable energy practices [15].

In 2015, Sakthivel et al. presented a pioneering hybrid MCDM strategy to ascertain the optimal biodiesel source and blending ratios. This innovative approach combined the analytical network process (ANP) with TOPSIS and VIKOR, enabling a comprehensive assessment of fuel blends. The study identified a B20 blend—comprising 20% biodiesel with 80% petroleum diesel—as the most favorable for achieving a balance between engine performance and environmental sustainability [16].

In 2020, Agarwal et al. underscored the importance of selecting the right biodiesel blend for internal combustion engines. Utilizing MCDM techniques like TOPSIS and VIKOR, the study delineated B75 as the optimal blend, highlighting its potential to enhance engine efficiency [17] significantly.

Similarly, Chaitanya et al. (2020) concentrated on minimizing engine emissions through the judicious selection of biodiesel blends. By deploying the AHP-TOPSIS method, the study evaluated various emissions to determine the most appropriate blend for different engine loads, advocating for B20 at low loads and B80 at high loads. This approach underscores the role of MCDM in aligning biofuel development with industrial requirements [18].

A further investigation into nano-emulsified diesel–biodiesel blends was conducted, employing MCDM techniques to identify blends that optimize emissions and engine efficiency across varying engine loads. The AHP-VIKOR methodology proved vital in establishing a preference order among blends, illustrating a robust framework for fuel blend selection [19].

In 2021, a hybrid multi-criteria decision-making (MCDM) framework was utilized in Iran to pinpoint the most suitable biomass resources for biofuel production. Incorporating techniques such as TOPSIS, ARAS, and WASPAS alongside ranking aggregation methods, this research highlighted the potential of MCDM in selecting sustainable biofuel sources [20].

Subsequently, Kügemann et al. developed a methodological framework for evaluating road transportation fuels and vehicles (RTFV) using MCDA. By integrating a life cycle sustainability assessment (LCSA), the framework broadened the analysis to encompass environmental, economic, and social dimensions, thereby enhancing decision-making transparency and stakeholder engagement in the fuel selection process [21].

At the core of recent investigations, a study on the antioxidant-treated Jatropha biodiesel’s impact on VCR diesel engine performance and emissions highlighted biodiesel’s potential as a sustainable fuel. Employing a blend enhanced with the antioxidant diphenylamine, significant reductions in NO_x emissions and brake-specific fuel consumption were observed, alongside improvements in engine performance, indicating the B30 + DPA blend’s efficacy in augmenting diesel engine efficiency while curtailing emissions [22].

Concluding this study, this research advances biodiesel blend selection methodologies by integrating a multi-criteria decision-making (MCDM) framework, incorporating grey relational analysis (GRA) with the technique for order preference by similarity to the ideal solution (TOPSIS). By evaluating biodiesel blends across environmental, performance, and economic criteria, this study proposes a detailed selection process. This innovative application of GRA-TOPSIS offers a tailored approach for the Egyptian context, signifying a notable step towards achieving sustainable and efficient fuel alternatives.

Paper Structure

This document is structured as follows: Section 1 introduces the study and its significance. Section 2 elaborates on the characteristics of the waste cooking oils and the transesterification process used in the study. Section 3 presents the GRA-TOPSIS method for evaluating the biodiesel blends. Section 4 outlines the overarching framework for biodiesel blend selection. Section 5 presents the results of the experiments and a comparative analysis of the different biodiesel blends. Section 6 discusses the implications of the findings. Finally, Section 7 provides a synopsis of the significant discoveries and proposes directions for subsequent research.

2. Test Fuel

The utilized cooking oils, procured from the local Egyptian market at economical prices, exhibit specific characteristics. These oils are primarily waste palm oil used for frying onions. The frying temperature ranges from 150 °C to 180 °C, with a frying period of 10–12 h daily. The oil is changed daily to ensure consistency [23,24].

Various methodologies are employed in biodiesel synthesis, including dilution, micro-emulsification, pyrolysis, and transesterification [25,26]. For this study, transesterification was selected due to its simplicity and widespread adoption as a method for biodiesel production. Figure 1 shows a simple illustration of the transesterification process. The advantage of the transesterification process is that it reduces the viscosity of vegetable oils and improves the fuel properties of fatty acid esters. This is because the viscosity of vegetable oils is much higher than that of diesel. There would be many problems if these vegetable oils were used directly in diesel engines as fuel.

The transesterification process was scrutinized under varying conditions: the molar ratio of alcohol to oil, duration and temperature of the reaction, agitation speed, and the nature and amount of the catalyst utilized. The parameters influencing the transesterification process included methanol at 20% weight by weight (w/w) of oil, potassium hydroxide (KOH) as a catalyst at 1% w/w of oil, a reaction temperature of 65 °C, a reaction time of 120 min, a stirrer speed of 400 revolutions per minute (rpm), and a separation time of 24 h.

This procedure yielded a 97% conversion rate for palm oil into biodiesel. The physicochemical properties of the produced biodiesel were within the recommended standard specifications for Egyptian diesel fuel and international biodiesel fuel for most properties except for the cetane number and calorific value. The cetane number, which measures the quality of fuel combustion, was 56 for the biodiesel produced, which was significantly higher than 45 for petroleum diesel, indicating a better combustion efficiency. The calorific value, referring to the energy available in the fuel, was slightly lower for biodiesel than for petroleum diesel. To address this, biodiesel was mixed with petroleum diesel in different proportions: B5, B10, etc.

Biodiesel derived from waste cooking oil (WCO) was amalgamated with diesel in varying proportions to create biodiesel blends of 5%, 10%, 20%, 30%, 40%, 50%, 75%, and 100%. The blending was executed using a compact electric motor, with the motor’s shaft and mixing apparatus integrated within the fuel containment, operating at a velocity of 300 rpm.

The physicochemical properties of the produced biodiesel are detailed below, as shown in

Table 1. Physicochemical properties of produced biodiesel compared to the Egyptian standards of petrodiesel fuel and biodiesel blends.

Test	B100	Egyptian Diesel Oil	B75	B50	B40	B30	B20	B10	B5
Density g/cm3 @ 15.56 °C	0.898	0.82–0.87	0.88	0.87	0.866	0.862	0.858	0.854	0.852
Kinematic viscosity cSt @ 40 °C	3.8	1.6–7	3.97	4.15	4.22	4.29	4.3	4.43	4.46
Flash point (°C)	175	> 55	147	118	106	95	83	72	66
Cloud point (°C)	7	2	5.75	4.5	4	3.5	3	2.5	2.25
Pour point (°C)	4	4.5–15	5.25	6.5	7	7.5	8	8.5	8.75
Cetane number	56	45	53	51	49	48.3	47.2	46.1	45.55
Total acid number (mg KOH/g)	0.2	0.062	0.165	0.131	0.117	0.103	0.089	0.075	0.069
Calorific value (MJ/kg)	42.37	Min. 44.3	42.85	43.33	43.53	43.7	43.9	44	44.2
Copper strip corrosion 3 h @ 50 °C	1 A	1 A	1 A	1 A	1 A	1 A	1 A	1 A	1 A

:

The cetane number of the biodiesel was 56, which was significantly higher than the 45 for petroleum diesel, indicating a better ignition quality and combustion efficiency. The calorific value of the biodiesel was slightly lower than that of petroleum diesel, necessitating its mixture with petroleum diesel in various proportions to optimize performance. The density and viscosity of the biodiesel were within the acceptable range specified for diesel fuels, ensuring proper fuel atomization and combustion. The flash point of the biodiesel was higher than that of petroleum diesel, enhancing its safety during storage and handling.

The blends of biodiesel and petroleum diesel were tested to determine their performance and emission characteristics, and the results are summarized as follows:

• Engine performance: The engine performance tests indicated that the biodiesel blends provided comparable power output to petroleum diesel. The B20 blend was particularly effective, providing a good balance between performance and emissions.
• Emissions: The biodiesel blends resulted in lower emissions of carbon monoxide (CO), hydrocarbons (HC), and particulate matter (PM) compared to petroleum diesel. However, nitrogen oxides (NO_x) emissions were slightly higher for the biodiesel blends.
• Fuel consumption: The fuel consumption for the biodiesel blends was slightly higher than that for petroleum diesel, which was attributed to the lower calorific value of the biodiesel.

3. Modeling Method

3.1. GRA-TOPSIS Method

Julong [27] proposed the grey relational analysis (GRA), a data analytic and geometric method used to determine the correlation between series. The technique aims to evaluate the relationship between the reference schemes. Some studies in the literature have adopted GRA for their research. This model is advantageous in analyzing the correlation between known and unknown information that is considered grey. Information is deemed white when precisely defined and black when there is no information available. The grey theory has found applications in various fields, such as manufacturing, process, and service operations. Additionally, it is advantageous in scenarios that involve multiple selection attributes and the selection process. Numerous investigations have incorporated the GRA methodology across various domains. For example, Sakthivel et al. implemented GRA techniques to determine the optimal automobile purchase model [28]. Subsequently, Sakthivel et al. [29] utilized GRA to identify the most suitable blend of fish oil and diesel. Most recently, in 2023, GRA was applied for the comparative analysis of various cathode materials in microbial electrolysis cells and for evaluating the air quality index using a GRA model incorporating cross-sequences, as reported by Lu et al. [30].

Hwang and Yoon developed TOPSIS, which is a relatively straightforward and speedy method with a systematic process [31]. It has been proven to be highly effective in resolving rank reversal issues. The fundamental principle of TOPSIS is to choose the decision that is closest to the ideal solution and furthest from the non-ideal one. The perfect and negative-ideal solutions are calculated by considering all other feasible alternatives [32]. The exhaust pollutants emitted by two-stroke petrol engines pose a significant threat to the environment. In recent years, there has been growing interest in using lubricants—a new generation of renewable and environmentally friendly lubricants derived from vegetables. In 2015, Dehghani et al. [33] analyzed the feasibility of using the technique for order of preference by similarity to the ideal solution (TOPSIS) method to create a scoring system that could assist in selecting the most suitable two-stroke lubricant. Evaluating the performance of employees against set standards is crucial in choosing the best candidates. This task is typically carried out by top-level management positions like the General Manager or Director, who use a decision-making method called the technique for order of preference by similarity to the ideal solution (TOPSIS). The criteria used by Rahim et al. [34] to evaluate the best employees included their job responsibilities, work discipline, work quality, and behavior.

Designers frequently encounter the challenge of selecting the most fitting design features from a variety of feasible options. This can be tedious, mainly when dealing with complex design specifications and numerous design alternatives for agricultural decision support systems related to fertilizer prescriptions. Hence, deciding on design attributes is typically considered a multifaceted decision-making issue. To tackle this problem, designers need a decision model that employs a standardized, efficient, and unbiased methodology to recognize and pick the most appropriate design attributes, as suggested by Motia et al. [35]. The model will significantly assist designers in optimizing the design process, enabling them to save valuable time and effort. In 2021, Shamsuzzoha et al. [36] recommended the fuzzy TOPSIS methodology as a viable option for selecting multifaceted projects in a corporate setting. Their research aimed to demonstrate fuzzy TOPSIS’s effectiveness in selecting multifaceted projects in organizations. To identify the causal factors of project complexity, the researchers conducted a meticulous literature review, which was subsequently analyzed using fuzzy TOPSIS, with input from three decision-makers. In 2023, Su et al. [37] proposed an improved TOPSIS model based on cumulative prospect theory. Their study aimed to provide a comprehensive decision-making method for investment decisions based on an environmental, social, and governance (ESG) performance evaluation of state-owned mining enterprises.

3.2. The Proposed Framework Algorithm

To implement the GRA-TOPSIS method, follow these steps:

Step 1: Normalization of the evaluation matrix: This process transforms different scales and units among various criteria into common measurable units for comparison using Equation (1).

$$r_{ij}={\displaystyle \frac{g_{ij}}{\sqrt{{\sum }_{j=1}^J{g}_{ij}^2}}}$$

(1)

Step 2: Determine the PIS and NIS using Equations (2) and (3), where $\overline{A}$ indicates the most preferable alternative and $\underline{A}$ indicates the least preferable alternative.

$$A_i^{*}=\{A_1^{*},\dots ,A_i^{*}\}=\{\left(ma{x}_j{A}_{ij}\right|i\in I),\left(mi{n}_j{A}_{ij}\right|i\in I^{″})\},$$

(2)

$$A_i^{-}=\{A_1^{-},\dots ,A_i^{-}\}=\{\left(mi{n}_j{A}_{ij}\right|i\in I),\left(ma{x}_j{A}_{ij}\right|i\in I^{″})\},$$

(3)

Step 3: To obtain the grey relation coefficient of each alternative to the positive ideal and negative ideal solutions, the PIS and NIS are taken as the referential sequence, and each alternative is considered as the comparative sequence. The solution is calculated to obtain $r(\overline{A}\left(j\right),A_i\left(j\right))$ and $r(\underline{A}\left(j\right),A_i\left(j\right))$ using Equations (4) and (5), respectively.

$$\overline{A}={\displaystyle \frac{mi{n}_{i}mi{n}_j|\overline{A}\left(j\right)-A_i\left(j\right)|+\xi ma{x}_{i}ma{x}_i|\overline{A}\left(j\right)-A_i\left(j\right)|}{|\overline{A}\left(j\right)-A_i\left(j\right)|+\xi ma{x}_{i}ma{x}_j|\overline{A}\left(j\right)-A_i\left(j\right)|}}$$

(4)

$$\underline{A}={\displaystyle \frac{mi{n}_{i}mi{n}_j|\underline{A}\left(j\right)-A_i\left(j\right)|+\xi ma{x}_{i}ma{x}_i|\underline{A}\left(j\right)-A_i\left(j\right)|}{|\underline{A}\left(j\right)-A_i\left(j\right)|+\xi ma{x}_{i}ma{x}_j|\underline{A}\left(j\right)-A_i\left(j\right)|}}$$

(5)

Step 4: To determine the grade of grey relation of each alternative to the PIS and NIS and its calculation, Equations (6) and (7) can be used:

For PIS:

$$r(\overline{A},A_i)-\sum _{j=1}^n{\varpi }_{j}r(\overline{A}\left(j\right),A_i\left(j\right))$$

(6)

For NIS:

$$r(\underline{A},A_i)-\sum _{j=1}^n{\varpi }_{j}r(\underline{A}\left(j\right),A_i\left(j\right))$$

(7)

$$\sum _{j=1}^n{\varpi }_j=1.$$

(8)

Step 5: Calculate the relative distance ${\kappa }_i$ of an alternative to the PIS, which is defined using Equation (9) as follows:

$${\kappa }_i-{\displaystyle \frac{r(\overline{A},A_i)}{r(\underline{A},A_i)}}$$

(9)

Step 6: The ranking of alternatives is based on their relative closeness, where a higher value of ${\kappa }_i$ indicates a higher priority for that alternative.

4. Proposed Framework

The proposed framework comprises three fundamental stages.

• The task involves identifying the criteria for performance and emissions.
• Observations are made to explore the criteria.
• We will utilize the GRA-TOPSIS method to rank the available alternatives.

The proposed methodology for selecting the best blend is outlined in Figure 2. Firstly, the alternative blends and their evaluation criteria are identified, and a decision hierarchy is established. Secondly, a single-cylinder four-stroke naturally aspirated compression-ignition engine is operated at a constant speed for different alternatives with variable loads to observe the performance, combustion, and emission characteristics. Lastly, the other options are ranked using the GRA-TOPSIS methodology based on observed readings and the relative weights of the evaluation criteria.

Evaluation Criteria for Optimal Fuel Mixture

As depicted in Figure 2, the evaluation criteria are organized hierarchically. The group decision-making approach facilitates the integration of insights from multiple internal combustion (IC) engine specialists and engine producers throughout the decision process. Below is an elaboration of the established criteria:

• CO: Emissions of carbon monoxide (CO) are influenced by the fuel’s oxygen and carbon content and combustion efficiency. CO emissions indicate incomplete combustion within the cylinder, primarily due to either insufficient oxygen relative to the theoretical need or a restricted combustion time.
• CO₂: Emissions of carbon dioxide (CO₂) from the diesel engine reflect the fuel’s combustion efficiency within the combustion chamber—effective combustion results in the conversion of most carbon into CO₂.
• NO_x: The generation of nitrogen oxides (NO_x) is contingent upon the peak temperature of the flame, ignition delay, and the availability of nitrogen and oxygen in the mixture undergoing combustion.
• HC: Hydrocarbons (HCs) in the fuel contribute to the combustion process in the presence of oxygen, with the excess HCs being emitted as unburned hydrocarbons.
• Particulate matter: Airborne pollution, known as particulate matter (PM), consists of particles of varying sizes and complexities.
• Engine power: In physics, power is defined as the rate at which work is performed. In the case of cars, horsepower is also a measure of speed. Engine power can be measured using units such as kilowatts (kW), Pferdestärke (PS), or horsepower (HP).
• Fuel consumption (FC): Fuel consumption refers to the quantity of fuel utilized to travel a specific distance. In the United States, this is measured in gallons per 100 miles, while in Europe and the rest of the world, it is measured in liters per 100 km. Fuel consumption increases for all types of fuels as the engine speed increases while maintaining a constant load.
• Engine noise: When a cylinder is fired in an engine, it produces a pulse that is emitted through the exhaust valves. Engines with more cylinders create pulses at a higher frequency, which results in the engine note.
• Tail noise: The sound produced by the exhaust system of vehicles with internal combustion engines is crucial. It should provide a good engine sound quality while complying with noise regulations and not causing disturbances. The intake and exhaust systems play a vital role in determining the engine noise character and sound pressure level (SPL), and they should be tuned to meet the required performance standards. The engine sound quality should convey information about the engine’s RPM, and the sound should be appropriate for the vehicle type, such as providing a robust and sporty sound during acceleration and being silent during constant-speed driving. This also applies to the exterior sound, where the sound character should match the vehicle’s brand identity.
• Exhaust gas temperature (EGT): The EGT measures the temperature at the back of an engine. It indicates how efficiently the heat energy of the fuel is being used. The location where the EGT is measured may vary between manufacturers, and each engine type has specific limits and norms. Therefore, it is an essential parameter in analyzing the emission values.

5. Experimental Results

This section evaluates the model’s utility by analyzing the selection of the optimal biodiesel blend within Egypt’s local cooking oil market.

5.1. Introduction to Biodiesel in Egypt

Egypt, as the host of COP 27 and a leader in Africa, symbolizes the continent’s quest for a viable energy transition strategy amidst growing climate concerns. The transition to alternative energy sources, such as biofuels, is seen as crucial for a sustainable future, though their economic viability remains debated [38].

Biofuel, a renewable energy source from organic materials, offers an alternative to fossil fuels, encompassing biodiesel, biogas, bioethanol, etc. This sector presents investment opportunities for both public and private entities [39].

Biofuels are posited to significantly enhance economic growth, creating jobs, especially in rural and agricultural areas [40]. Egypt’s robust agriculture can support the biofuel industry without resource scarcity, potentially boosting the economy.

A 2012 study by Moschini et al. titled “Economics of Biofuels: An Overview of Policies, Impacts, and Prospects” discusses biofuels’ economic benefits, particularly in agriculture, supporting the sector and encouraging rural development [41].

Egypt’s burgeoning biodiesel industry benefits from local production and government investment in Jatropha. Despite high costs, a 2015 study by SolimanHe et al. highlighted Jatropha’s biodiesel production potential and environmental benefits, albeit with lower-than-expected profits [42].

Ibrahim Farouk et al. emphasize Egypt’s biofuel pricing advantage, which is attributed to lower production costs compared to Europe, enhancing its appeal to international markets. Egypt’s extensive experience in vegetable oil production since the 1950s provides a technological advantage in biofuel production [43].

The upcoming COP 27 is seen as an opportunity to attract vital investments and partnerships for the biodiesel industry, aiming to establish Egypt as a biofuel hub by 2030 [44].

Egypt’s strategic location near Europe positions it as an ideal biofuel exporter, catering to European demand for sustainable fuel. Despite progress, further development is essential for Egypt to become a significant market player. However, its commitment to The Paris Agreement and potential for exports offer a positive outlook [45].

Biofuels represent an environmentally friendly and economically beneficial option for Egypt’s energy transition, emphasizing nature-based solutions to complex challenges [46].

5.2. Experimental Setup

The experimental investigations were conducted using a single-cylinder, air-cooled diesel engine of $TD111$ type (manufactured by ‘Robin’-Fuji DY23D). The detailed technical specifications of the engine are presented in

Table 2. The technical specifications of the engine.

Model	‘Robin’-Fuji DY23D.
Type	4 cycle, overhead valve, single cylinder
Piston displacement	230 cm3.
Bore/stoke	70 × 60 mm.
Compression ratio	21
Nominal output	3.5 kW at 3600 rev/min.
Maximum torque	10.5 Nm at 2200 rev/min.
Cooling	Forced air cooling
Lubrication	Forced oil lubrication
Injection type	Direct injection (DI)

. For engine load applications, a hydraulic dynamo meter, TechQuipment $TD114$, was utilized. Emission parameters such as carbon monoxide (CO), carbon dioxide (CO₂), hydrocarbons (HC), and nitrogen oxides (NO_x) were quantified using a Brain Bee S.P.A, AGS-688 Gas Analyzer, Rudolf Diesel 10/a, Parma, 43122, Italy A Lucas Smoke Meter was used to measure the particle matter ($PM$) concentrations. The operational ranges of the gas analyzer are documented in

Table 3. Gas analyzer’s measurement fields.

Constituent	Symbol	Scale	Unit	Resolution
Carbon monoxide	CO	0–9.99	% vol.	0.01
Carbon dioxide	CO2	0–19.9	% vol.	0.1
Total hydrocarbon	HC	0–9999	Ppm	1
Oxygen	O2	0-25	% vol.	0.01
Oxides of nitrogen	NOx	0–5000	Ppm	10

. Acoustic emissions from both the engine and exhaust were measured using a sound level meter ($SLM$) model RO-1350A, with its specifications detailed in

Table 4. Sound level meter specifications.

Maximum sound level	135 db
Minimum sound level	35 db
Resolution	0.1 db
Accuracy class	IEC 651 Type 2
Weighting	200 g
Display type	LCD
Supply	9 V PP3-type battery supplied
Dimensions (mm):	240 × 68 × 25
Maximum frequency	12 kHz
Maximum operating temperature	+50 °C
Minimum frequency	30 Hz
Minimum operating temperature	0 °C
Model numer	RO 1350A

. The schematic layout of the testing rig is depicted in Figure 3, and a photograph of the SLM is shown in Figure 4 [23,24].

5.3. Criteria for Selecting the Best Blend

This study utilizes a literature review to identify evaluation criteria for the best biodiesel blend selection, incorporating a hierarchical approach and group decision-making to integrate expert opinions from the IC engine and manufacturing sectors [47].

CO: carbon monoxide

CO₂: Carbon dioxide

NO_x: Nitrogen oxides

HC: Hydrocarbon

PM: Particulate matter

EP: Engine power

FC: Fuel consumption

EN: Engine noise

TN: Tail noise

EGT: Exhaust gas temperature

The GRA-TOPSIS method is proposed for selecting the best blend among the alternative blends.

5.4. GRA-TOPSIS Computation

This section applies the suggested model in a real-world context to select from various biodiesel blend options. The systematic choice of biodiesel blends is crucial for Egypt to support its economic growth. A panel assessed eight different fuel blend alternatives: Diesel, B5, B10, B20, B30, B50, B75, and B100, formulated by adjusting the biodiesel’s diesel content. The evaluation criteria included CO, CO₂, NO_x, HC, PM, EP, FC, EN, tail noise, and EGT, as detailed in

Table 5. Observational data on combustion, performance, and emissions from engine tests across diverse alternative blends.

Load %	Fuel	CO, %vol	CO2, %vol	NOx, ppm	HC, ppm	PM, ppm	Engine Power, Kw	Fuel Cons., kg/h	Engine Noise, db	Tail Noise, db	Exhaust Temp. C
0%	Diesel	0.04	1.4	76	18	17.5	0.23	0.228	90	66	95
	B5	0.06	1.1	20	31	7.8	0.228	0.229	89	67.5	98
	B10	0.05	1.3	28	38	4.7	0.221	0.232	88.7	67.4	105
	B20	0.05	1.1	37	34	4.4	0.211	0.238	90.8	68.1	108
	B30	0.05	1.2	11	37	4.27	0.2	0.241	91.7	69.3	115
	B50	0.05	1.22	14	28	6.9	0.191	0.249	92.1	71.5	120
	B75	0.05	1.4	16	22	10.1	0.182	0.232	94.7	79.4	110
	B100	0.06	1.3	20	20	7.2	0.17	0.239	95.1	81.3	120
15%	Diesel	0.04	1.6	89	42	17.3	0.354	0.231	90.7	69	115
	B5	0.05	1.4	43	29	6	0.341	0.228	89.3	68.3	120
	B10	0.06	1.6	47	43	2.9	0.311	0.234	90.8	68.8	125
	B20	0.05	1.6	49	38	6.8	0.294	0.241	91.3	69.4	125
	B30	0.08	1.6	55	38	4.5	0.286	0.253	92.1	69.8	130
	B50	0.06	2.1	46	29	9.6	0.262	0.278	94.6	73.7	130
	B75	0.04	1.7	48	25	9.6	0.255	0.289	94.2	80.2	125
	B100	0.06	1.8	49	19	7.8	0.241	0.317	94.3	81.6	125
25%	Diesel	0.04	2.2	169	18	23.1	0.57	0.255	92	70.4	120
	B5	0.06	1.4	46	30	5.9	0.56	0.258	91.3	70	125
	B10	0.06	1.5	52	34	6.9	0.521	0.263	91.8	70.2	125
	B20	0.05	1.6	59	39	10.3	0.495	0.269	91	70.4	135
	B30	0.05	1.6	66	37	7.8	0.421	0.287	91.7	70.5	140
	B50	0.6	1.8	81	32	8.5	0.383	0.291	92.5	72	135
	B75	0.6	1.9	89	27	9.4	0.364	0.31	94	74.1	135
	B100	0.07	2.2	111	31	11.7	0.311	0.342	94.8	78.2	140
35%	Diesel	0.07	2.4	146	48	26.7	1.3	0.278	92.8	69	140
	B5	0.05	1.5	155	27	8.9	1.24	0.292	89.3	68.3	150
	B10	0.05	1.6	161	45	10.1	1.09	0.311	90.8	68.8	135
	B20	0.05	1.8	159	39	11.7	1.01	0.332	91.3	69.4	125
	B30	0.05	2.1	166	46	21.6	0.987	0.358	92.1	69.8	155
	B50	0.06	2.2	177	26	13.9	0.94	0.398	94.6	73.7	150
	B75	0.06	2.7	179	26	13.1	0.951	0.411	94.2	80.2	150
	B100	0.07	3.3	201	30	12.6	0.943	0.478	94.3	81.6	125
50%	Diesel	0.07	2.8	203	20	29.3	1.42	0.312	93.2	71.5	145
	B5	0.05	1.5	62	27	12.4	1.4	0.329	93	72	150
	B10	0.06	1.8	71	31	11.1	1.34	0.387	93.3	73.4	145
	B20	0.05	1.8	79	37	28.2	1.31	0.399	93.9	74.5	155
	B30	0.08	2.9	59	42	21.6	1.28	0.426	94.6	71.9	165
	B50	0.07	2.9	144	35	16.8	1.19	0.439	94	75	160
	B75	0.06	2.7	168	26	15.1	1.1	0.489	94.4	82.2	150
	B100	0.07	3.1	179	30	12.6	0.91	0.578	94.7	83.4	125
65%	Diesel	0.14	2.6	179	22	41	1.316	1.131	93.7	70.7	150
	B5	0.06	1.8	101	19	15.6	1.312	1.137	93.2	69.4	150
	B10	0.05	1.7	67	43	3.6	1.287	1.149	90.8	68.7	135
	B20	0.05	1.8	79	37	28.2	1.272	1.178	94.7	70.8	125
	B30	0.08	2.9	59	42	21.6	1.202	1.21	94.6	71.9	165
	B50	0.05	2.3	149	34	10.6	1.047	1.292	94.9	77.2	140
	B75	0.09	3	178	31	23.2	0.986	1.329	95.5	82.9	155
	B100	0.18	3.6	180	33	15.4	0.912	1.362	96.4	83.2	150

.

Following this, the methodology outlined in the pseudo-code of the suggested framework, detailed in Equation (1), is implemented as described.

Step 1: The initial step involves the normalization of the experimental data, utilizing Equation (1), as presented in Table 5. The outcomes of this normalization are systematically organized and displayed in

Table 6. Normalized decision matrix ($r_{ij}$).

Load %	Fuel	CO, %vol	CO2, %vol	NOx, ppm	HC, ppm	PM, ppm	Engine Power, Kw	Fuel Cons., kg/h	Engine Noise, db	Tail Noise, db	Exhaust Temp. C
No Load 0%	Diesel	0.274	0.393	0.788	0.216	0.698	0.396	0.341	0.347	0.326	0.307
	B5	0.411	0.309	0.207	0.372	0.311	0.392	0.342	0.343	0.333	0.317
	B10	0.342	0.365	0.290	0.456	0.187	0.380	0.347	0.342	0.333	0.339
	B20	0.342	0.309	0.383	0.408	0.175	0.363	0.356	0.350	0.336	0.349
	B30	0.342	0.337	0.114	0.444	0.170	0.344	0.360	0.354	0.342	0.372
	B50	0.342	0.343	0.145	0.336	0.275	0.329	0.372	0.355	0.353	0.388
	B75	0.342	0.393	0.165	0.264	0.402	0.313	0.347	0.365	0.392	0.356
	B100	0.411	0.365	0.207	0.240	0.287	0.292	0.357	0.367	0.401	0.388
15%	Diesel	0.250	0.335	0.571	0.438	0.675	0.423	0.313	0.347	0.335	0.326
	B5	0.313	0.293	0.276	0.302	0.234	0.408	0.309	0.342	0.331	0.340
	B10	0.376	0.335	0.301	0.449	0.113	0.372	0.317	0.348	0.334	0.355
	B20	0.313	0.335	0.314	0.396	0.265	0.351	0.326	0.350	0.337	0.355
	B30	0.501	0.335	0.353	0.396	0.175	0.342	0.343	0.353	0.339	0.369
	B50	0.376	0.440	0.295	0.302	0.375	0.313	0.377	0.362	0.358	0.369
	B75	0.250	0.356	0.308	0.261	0.375	0.305	0.392	0.361	0.389	0.355
	B100	0.376	0.377	0.314	0.198	0.304	0.288	0.429	0.361	0.396	0.355
25%	Diesel	0.046	0.432	0.647	0.201	0.702	0.436	0.315	0.352	0.345	0.321
	B5	0.069	0.275	0.176	0.335	0.179	0.428	0.319	0.349	0.343	0.334
	B10	0.069	0.294	0.199	0.380	0.209	0.398	0.325	0.351	0.344	0.334
	B20	0.058	0.314	0.226	0.436	0.313	0.378	0.332	0.348	0.345	0.361
	B30	0.058	0.314	0.253	0.414	0.237	0.322	0.355	0.350	0.346	0.374
	B50	0.698	0.353	0.310	0.358	0.258	0.293	0.360	0.353	0.353	0.361
	B75	0.698	0.373	0.341	0.302	0.285	0.278	0.383	0.359	0.363	0.361
	B100	0.081	0.432	0.425	0.346	0.355	0.237	0.423	0.362	0.383	0.374
35%	Diesel	0.426	0.373	0.305	0.458	0.593	0.431	0.270	0.354	0.335	0.349
	B5	0.304	0.233	0.3247	0.258	0.197	0.411	0.284	0.341	0.331	0.374
	B10	0.304	0.249	0.337	0.430	0.224	0.361	0.303	0.347	0.334	0.336
	B20	0.304	0.280	0.333	0.372	0.260	0.335	0.323	0.349	0.337	0.311
	B30	0.304	0.327	0.333	0.439	0.480	0.327	0.348	0.352	0.339	0.386
	B50	0.365	0.342	0.370	0.248	0.309	0.311	0.387	0.361	0.358	0.374
	B75	0.365	0.420	0.374	0.248	0.291	0.315	0.400	0.360	0.389	0.374
	B100	0.426	0.513	0.421	0.286	0.280	0.312	0.465	0.360	0.396	0.311
50%	Diesel	0.383	0.394	0.540	0.223	0.529	0.400	0.258	0.350	0.334	0.342
	B5	0.273	0.211	0.165	0.301	0.223	0.394	0.272	0.350	0.336	0.354
	B10	0.328	0.253	0.189	0.346	0.200	0.377	0.320	0.351	0.343	0.342
	B20	0.273	0.253	0.210	0.413	0.509	0.369	0.329	0.353	0.348	0.365
	B30	0.438	0.408	0.157	0.468	0.390	0.360	0.352	0.356	0.336	0.389
	B50	0.383	0.408	0.383	0.390	0.303	0.335	0.363	0.353	0.350	0.377
	B75	0.328	0.380	0.447	0.290	0.272	0.310	0.404	0.355	0.384	0.354
	B100	0.383	0.437	0.477	0.33	0.227	0.256	0.478	0.356	0.389	0.295
65%	Diesel	0.502	0.361	0.473	0.231	0.641	0.395	0.326	0.351	0.335	0.361
	B5	0.215	0.250	0.267	0.199	0.244	0.394	0.327	0.349	0.329	0.361
	B10	0.179	0.236	0.177	0.452	0.056	0.386	0.331	0.340	0.325	0.325
	B20	0.179	0.250	0.209	0.389	0.441	0.382	0.339	0.355	0.335	0.301
	B30	0.287	0.402	0.156	0.441	0.337	0.361	0.348	0.354	0.340	0.397
	B50	0.179	0.319	0.394	0.357	0.165	0.314	0.372	0.356	0.366	0.337
	B75	0.323	0.416	0.471	0.326	0.362	0.296	0.383	0.358	0.393	0.373
	B100	0.646	0.500	0.476	0.347	0.240	0.274	0.392	0.361	0.394	0.361

.

Step 2: This step is dedicated to the identification of the positive ideal solution (PIS) $\overline{A}$, indicating the most favorable option, and the negative ideal solution (NIS) $\underline{A}$, representing the least-favorable options. These determinations are made through the application of Equations (2) and (3), with the results provided in

Table 7. PIS $A^{+}$ values.

Load %	CO, %vol	CO2, %vol	NOx, ppm	HC, ppm	PM, ppm	Engine Power, Kw	Fuel Cons., kg/h	Engine Noise, db	Tail Noise, db	Exhaust Temp. C
0%	0.274	0.309	0.114	0.216	0.170	0.396	0.341	0.342	0.326	0.307
15%	0.250	0.293	0.276	0.198	0.113	0.423	0.309	0.342	0.331	0.326
25%	0.046	0.275	0.176	0.201	0.179	0.436	0.315	0.348	0.343	0.321
35%	0.304	0.233	0.305	0.248	0.197	0.431	0.271	0.341	0.331	0.311
50%	0.273	0.211	0.157	0.223	0.200	0.400	0.258	0.350	0.334	0.295
65%	0.179	0.236	0.156	0.199	0.056	0.395	0.326	0.341	0.325	0.302

and

Table 8. NIS $A^{-}$ values.

Load %	CO, %vol	CO2, %vol	NOx, ppm	HC, ppm	PM, ppm	Engine Power, Kw	Fuel Cons., kg/h	Engine Noise, db	Tail Noise, db	Exhaust Temp. C
0%	0.411	0.393	0.787	0.456	0.698	0.292	0.372	0.367	0.401	0.388
15%	0.501	0.440	0.571	0.449	0.675	0.288	0.429	0.362	0.396	0.369
25%	0.698	0.432	0.647	0.436	0.702	0.237	0.423	0.362	0.383	0.374
35%	0.426	0.513	0.421	0.458	0.593	0.311	0.465	0.361	0.396	0.386
50%	0.438	0.437	0.541	0.468	0.529	0.256	0.478	0.356	0.389	0.389
65%	0.646	0.500	0.476	0.452	0.641	0.274	0.392	0.361	0.394	0.397

.

Step 3: To calculate the grey relation coefficient for each alternative to the PIS and NIS, this step takes the PIS and NIS as reference sequences, with each alternative acting as a comparative sequence. The coefficients $r(\overline{A}\left(j\right),A_i\left(j\right))$ and $r(\underline{A}\left(j\right),A_i\left(j\right))$ are derived using Equations (4) and (5), respectively, and the detailed outcomes are presented in

Table 9. PIS—Grey relation coefficient.

PIS
Alternatives Criteria		Diesel	B5	B10	B20	B30	B50	B75	B100
0%	CO, %vol	1.000	0.333	0.499	0.499	0.499	0.499	0.499	0.333
	CO2, %vol	0.335	1.000	0.431	1.000	0.602	0.558	0.335	0.431
	NOx, ppm	0.333	0.783	0.656	0.555	1.000	0.915	0.866	0.783
	HC, ppm	1.000	0.434	0.333	0.384	0.344	0.499	0.713	0.831
	PM, ppm	0.333	0.652	0.939	0.980	1.000	0.715	0.532	0.693
	Engine power, Kw	1.000	0.949	0.777	0.618	0.504	0.438	0.387	0.335
	Fuel cons., kg/h	1.000	1.000	0.732	0.522	0.456	0.342	0.732	0.498
	Engine noise, db	0.724	0.919	1.000	0.620	0.533	0.501	0.363	0.348
	Tail noise, db	1.000	0.837	0.846	0.786	0.700	0.584	0.365	0.335
	Exhaust temp., C	1.000	0.809	0.560	0.494	0.389	0.337	0.459	0.337
15%	CO, %vol	1.000	0.669	0.502	0.669	0.335	0.502	1.000	0.502
	CO2, %vol	0.639	1.00	0.639	0.639	0.639	0.335	0.541	0.469
	NOx, ppm	0.333	1.000	0.852	0.793	0.657	0.884	0.821	0.793
	HC, ppm	0.343	0.546	0.334	0.388	0.388	0.546	0.667	1.000
	PM, ppm	0.333	0.699	1.000	0.648	0.818	0.518	0.518	0.595
	Engine power, Kw	1.000	0.826	0.574	0.490	0.458	0.384	0.366	0.336
	Fuel cons., kg/h	0.937	1.000	0.881	0.775	0.641	0.472	0.423	0.334
	Engine noise, db	0.670	1.000	0.654	0.587	0.504	0.349	0.367	0.362
	Tail noise, db	0.907	1.000	0.932	0.862	1.000	0.560	0.367	0.341
	Exhaust temp., C	1.000	0.611	0.440	0.440	0.343	0.343	0.440	0.440
25%	CO, %vol	1.000	0.933	0.933	0.965	0.965	0.333	0.333	0.903
	CO2, %vol	0.334	1.000	0.800	0.667	0.667	0.501	0.445	0.334
	NOx, ppm	0.333	1.000	0.911	0.825	0.755	0.637	0.589	0.486
	HC, ppm	1.000	0.468	0.397	0.334	0.357	0.429	0.539	0.448
	PM, ppm	0.333	1.000	0.896	0.662	0.819	0.768	0.711	0.597
	Engine power, Kw	1.000	0.930	0.727	0.634	0.465	0.409	0.386	0.333
	Fuel cons., kg/h	1.000	0.936	0.846	0.759	0.579	0.550	0.445	0.336
	Engine noise, db	0.664	0.868	0.712	1.000	0.739	0.569	0.397	0.342
	Tail noise, db	0.914	1.000	0.955	0.914	0.895	0.681	0.511	0.343
	Exhaust temp., C	1.000	0.669	0.669	0.403	0.336	0.403	0.403	0.336
35%	CO, %vol	0.334	1.000	1.000	1.000	1.000	0.501	0.507	0.334
	CO2, %vol	0.501	1.000	0.900	0.751	0.601	0.564	0.430	0.334
	NOx, ppm	1.000	0.757	0.652	0.683	0.683	0.475	0.459	0.338
	HC, ppm	0.334	0.917	0.368	0.460	0.356	1.000	1.000	0.734
	PM, ppm	0.334	1.000	0.881	0.762	0.413	0.641	0.680	0.707
	Engine power, Kw	1.000	0.755	0.463	0.384	0.366	0.334	0.341	0.336
	Fuel cons., kg/h	1.000	0.879	0.753	0.650	0.556	0.455	0.429	0.333
	Engine noise, db	0.449	1.000	0.655	0.588	0.505	0.350	0.368	0.363
	Tail noise, db	0.907	1.000	0.932	0.862	1.000	0.560	0.367	0.341
	Exhaust temp., C	0.509	0.383	0.608	1.000	0.341	0.383	0.383	1.000
50%	CO, %vol	0.432	1.000	0.604	1.000	0.337	0.432	0.604	0.432
	CO2, %vol	0.382	1.000	0.728	0.728	0.365	0.365	0.401	0.334
	NOx, ppm	0.333	1.000	0.893	0.815	1.000	0.459	0.398	0.375
	HC, ppm	1.000	0.611	0.500	0.393	0.334	0.423	0.647	0.524
	PM, ppm	0.334	0.875	1.000	0.348	0.465	0.615	0.695	0.858
	Engine power, Kw	1.000	0.935	0.767	0.703	0.650	0.529	0.445	0.334
	Fuel cons., kg/h	1.000	0.886	0.639	0.604	0.538	0.511	0.429	0.333
	Engine noise, db	0.823	1.000	0.756	0.508	0.367	0.482	0.399	0.353
	Tail noise, db	1.000	0.923	0.761	0.668	0.937	0.633	0.361	0.337
	Exhaust temp., C	0.499	0.444	0.499	0.399	0.333	0.363	0.444	1.000
65%	CO, %vol	0.420	0.867	1.000	1.000	0.684	1.000	0.619	0.334
	CO2, %vol	0.514	0.908	1.000	0.904	0.442	0.613	0.422	0.333
	NOx, ppm	0.335	0.590	0.883	0.751	1.000	0.402	0.337	0.333
	HC, ppm	0.801	1.000	0.335	0.392	0.335	0.447	0.502	0.464
	PM, ppm	0.333	0.609	1.000	0.432	0.509	0.727	0.488	0.613
	Engine power, Kw	1.000	0.996	0.887	0.832	0.646	0.432	0.382	0.336
	Fuel cons., kg/h	1.000	0.949	0.846	0.710	0.593	0.417	0.368	0.333
	Engine noise, db	0.511	0.562	1.000	0.433	0.440	0.420	0.386	0.344
	Tail noise, db	0.789	0.914	1.000	0.781	0.700	0.468	0.345	0.340
	Exhaust temp., C	0.452	0.452	0.682	1.000	0.338	0.584	0.407	0.452

and

Table 10. NIS—Grey relation coefficient.

NIS
Alternatives Criteria		Diesel	B5	B10	B20	B30	B50	B75	B100
0%	CO, %vol	0.333	1.000	0.501	0.501	0.501	0.501	0.501	1.000
	CO2, %vol	1.000	0.338	0.613	0.338	0.436	0.462	1.000	0.613
	NOx, ppm	1.000	0.368	0.405	0.456	0.334	0.344	0.352	0.368
	HC, ppm	0.335	0.593	1.000	0.721	0.919	0.503	0.387	0.359
	PM, ppm	1.000	0.405	0.340	0.335	0.333	0.384	0.472	0.391
	Engine power, Kw	0.339	0.347	0.376	0.429	0.506	0.594	0.719	1.000
	Fuel cons., kg/h	0.352	0.364	0.405	0.523	0.612	1.000	0.405	0.550
	Engine noise, db	0.395	0.352	0.341	0.438	0.499	0.532	0.930	1.000
	Tail noise, db	0.341	0.366	0.363	0.376	0.399	0.450	0.834	1.000
	Exhaust temp., C	0.336	0.366	0.460	0.517	0.726	1.000	0.563	1.000
15%	CO, %vol	0.335	0.403	0.504	0.403	1.000	0.504	0.335	0.504
	CO2, %vol	0.414	0.335	0.414	0.414	0.414	1.000	0.469	0.542
	NOx, ppm	1.000	0.335	0.355	0.367	0.405	0.350	0.361	0.367
	HC, ppm	0.923	0.461	1.000	0.706	0.706	0.461	0.400	0.333
	PM, ppm	1.000	0.390	0.334	0.408	0.361	0.484	0.484	0.432
	Engine power, Kw	0.335	0.363	0.448	0.518	0.558	0.730	0.802	1.000
	Fuel cons., kg/h	0.346	0.338	0.354	0.375	0.417	0.544	0.628	1.000
	Engine noise, db	0.421	0.344	0.428	0.466	0.544	0.951	0.963	1.000
	Tail noise, db	0.350	0.337	0.346	0.357	0.365	0.464	0.845	1.000
	Exhaust temp. C	0.337	0.435	0.611	0.611	1.000	1.000	0.611	0.611
25%	CO, %vol	0.333	0.341	0.341	0.337	0.337	1.000	1.000	0.345
	CO2, %vol	1.000	0.335	0.366	0.403	0.403	0.504	0.577	1.000
	NOx, ppm	1.000	0.334	0.346	0.360	0.375	0.413	0.436	0.517
	HC, ppm	0.334	0.541	0.681	1.000	0.845	0.603	0.468	0.570
	PM, ppm	1.000	0.334	0.347	0.403	0.360	0.371	0.386	0.431
	Engine power, Kw	0.336	0.345	0.384	0.416	0.544	0.645	0.712	1.000
	Fuel cons., kg/h	0.377	0.368	0.386	0.411	0.383	0.611	0.715	1.000
	Engine noise, db	0.453	0.391	0.433	0.369	0.424	0.511	0.830	1.000
	Tail noise, db	0.359	0.347	0.353	0.359	0.363	0.417	0.527	1.000
	Exhaust temp., C	0.343	0.413	0.413	0.697	1.000	0.697	0.697	1.000
35%	CO, %vol	1.000	0.333	0.333	0.333	0.333	0.500	0.500	1.000
	CO2, %vol	0.503	0.335	0.348	0.377	0.431	0.453	0.605	1.000
	NOx, ppm	0.333	0.374	0.407	0.395	0.395	0.534	0.555	1.000
	HC, ppm	1.000	0.346	0.795	0.555	0.857	0.335	0.335	0.382
	PM, ppm	1.000	0.334	0.350	0.374	0.639	0.412	0.397	0.388
	Engine power, Kw	0.333	0.379	0.550	0.724	0.796	1.000	0.943	0.983
	Fuel cons., kg/h	0.335	0.352	0.377	0.409	0.458	0.561	0.604	1.000
	Engine noise, db	0.637	0.345	0.429	0.467	0.544	0.955	0.963	1.000
	Tail noise, db	0.350	0.337	0.346	0.357	0.365	0.464	0.845	1.000
	Exhaust temp., C	0.513	0.775	0.438	0.340	1.000	0.775	0.775	0.340
50%	CO, %vol	0.604	0.334	0.430	0.334	1.000	0.604	0.430	0.604
	CO2, %vol	0.728	0.333	0.381	0.381	0.801	0.801	0.667	1.000
	NOx, ppm	1.000	0.338	0.352	0.367	0.333	0.549	0.672	0.749
	HC, ppm	0.335	0.426	0.504	0.695	1.000	0.617	0.410	0.482
	PM, ppm	1.000	0.350	0.333	0.893	0.542	0.421	0.390	0.353
	Engine power, Kw	0.335	0.344	0.374	0.392	0.410	0.479	0.575	1.000
	Fuel cons., kg/h	0.333	0.348	0.410	0.426	0.466	0.489	0.599	1.000
	Engine noise, db	0.393	0.359	0.413	0.589	1.000	0.634	0.913	0.892
	Tail noise, db	0.344	0.355	0.386	0.416	0.353	0.430	0.884	1.000
	Exhaust temp., C	0.505	0.578	0.505	0.675	1.000	0.812	0.578	0.336
65%	CO, %vol	0.619	0.351	0.333	0.333	0.394	0.333	0.419	1.000
	CO2, %vol	0.488	0.346	0.333	0.346	0.577	0.423	0.614	1.000
	NOx, ppm	0.989	0.435	0.349	0.375	0.334	0.663	0.973	1.000
	HC, ppm	0.364	0.334	1.000	0.670	0.929	0.574	0.502	0.547
	PM, ppm	1.000	0.424	0.333	0.594	0.491	0.381	0.513	0.422
	Engine power, Kw	0.333	0.335	0.350	0.359	0.410	0.599	0.731	1.000
	Fuel cons., kg/h	0.339	0.345	0.358	0.393	0.440	0.639	0.802	1.000
	Engine noise, db	0.551	0.503	0.355	0.682	0.666	0.715	0.840	1.000
	Tail noise, db	0.373	0.349	0.338	0.375	0.397	0.558	0.989	1.000
	Exhaust temp. C	0.961	0.961	0.926	0.903	1.000	0.937	0.974	0.961

.

Step 4: To ascertain the grey relation grades of each alternative concerning the PIS and NIS, calculations are performed using Equations (6) and (7), respectively. The outcomes of these calculations are presented in

Table 11. PIS—Grade of grey relation of each alternative.

Alternatives
PIS
Load	Diesel	B5	B10	B20	B30	B50	B75	B100
0%	0.834008	0.68486	0.620825	0.594875	0.541341	0.506731	0.542906	0.53322
15%	0.677057	0.739079	0.602257	0.564207	0.518041	0.473721	0.569517	0.588976
25%	0.824281	0.789834	0.712438	0.626605	0.594418	0.501206	0.483488	0.466317
35%	0.520669	0.847483	0.669747	0.712195	0.51952	0.600153	0.587785	0.590402
50%	0.698708	0.781893	0.661906	0.545067	0.443669	0.466289	0.530461	0.570679
65%	0.611309	0.781412	0.765402	0.676217	0.489992	0.571023	0.453124	0.421888

and

Table 12. NIS—Grade of grey relation of each alternative.

Alternatives
NIS
Load	Diesel	B5	B10	B20	B30	B50	B75	B100
0%	0.483568	0.493329	0.560649	0.509861	0.609658	0.60105	0.55936	0.69238
15%	0.597721	0.398929	0.579737	0.516884	0.654961	0.64191	0.55058	0.60078
25%	0.491797	0.405714	0.450457	0.581687	0.598783	0.60625	0.62357	0.73136
35%	0.719892	0.414669	0.490959	0.437648	0.66994	0.56045	0.58863	0.66131
50%	0.526268	0.402582	0.433342	0.588225	0.798019	0.60178	0.54874	0.61965
65%	0.611424	0.468802	0.59545	0.579467	0.667895	0.59191	0.68104	0.80775

.

Step 5: The next phase involves calculating the relative closeness indicator $C_i$ for all alternatives based on Equation (9). The results of these calculations are compiled in

Table 13. Relative closeness $C_i$ of alternatives.

Blends	0%	Rank	15%	Rank	25%	Rank	35%	Rank	50%	Rank	65%	Rank
Diesel	1.7246964	1	1.132731	2	1.676059	2	0.72326	8	1.32767	3	0.9998119	4
B5	1.3882419	2	1.852658	1	1.946775	1	2.04376	1	1.9422	1	1.6668274	1
B10	1.1073328	4	1.038845	4	1.581589	3	1.36416	3	1.52744	2	1.2854178	2
B20	1.1667396	3	1.091554	3	1.07722	4	1.62732	2	0.92663	5	1.1669638	3
B30	0.8879421	6	0.790949	7	0.99271	5	0.77547	7	0.55596	8	0.7336363	6
B50	0.8430791	7	0.737987	8	0.826738	6	1.07083	4	0.77485	7	0.9647191	5
B75	0.9705842	5	1.034395	5	0.77535	7	0.99856	5	0.9667	4	0.6653403	7
B100	0.7701273	8	0.980359	6	0.637603	8	0.89278	6	0.92098	6	0.5222989	8

.

Step 6: In the final step, the alternatives are ranked based on their relative closeness values $C_i$, where a more significant $C_i$ value implies a higher ranking and preference for the alternative.

The GRA-TOPSIS method is proposed to select the best blend among the alternative blends. The first step of the GRA-TOPSIS is normalizing the experimental readings using Equation (1) from Table 5. The normalized decision matrix is tabulated in Table 6.

After a normalized decision matrix is formed, the identification of the positive ideal solution (PIS) $A^{+}$, indicating the most favorable option, and the negative ideal solution (NIS) $A^{-}$ values, representing all the alternatives, are determined using Equations (2) and (3) and are tabulated in Table 7 and Table 8.

The results of the proposed methodology are tabulated in

Table 14. Summary of results.

Blends	0%	15%	25%	35%	50%	65%	Harmonic Mean Ranking of the Loads
Diesel	1	2	8	3	4	4	4
B5	2	1	1	1	1	1	1
B10	4	4	3	3	2	2	8
B20	3	3	4	2	5	3	7
B30	6	7	5	1	7	8	2
B50	7	8	6	4	7	5	6
B75	5	5	7	5	4	7	5
B100	8	6	8	6	6	8	3

. The preference order of alternative blends is $B5>B30>B100>Diesel>B75>B50>B20>B10$. The decision-maker can choose B5 as the optimum blend to run IC engines.

6. Discussion

The findings of this study underscore the potential of biodiesel derived from waste cooking oil (WCO) as a viable alternative to conventional diesel fuel. The evaluation framework, integrating grey relational analysis (GRA) with the technique for order preference by similarity to the ideal solution (TOPSIS), facilitated a comprehensive assessment of various biodiesel blends, providing valuable insights into their performance characteristics.

Our analysis of eight biodiesel blends (Diesel, B5, B10, B20, B30, B50, B75, and B100) indicated that blends with lower biodiesel contents, specifically B5 and B20, exhibited superior performances across multiple metrics. Notably, the B5 blend emerged as the most balanced option, offering an optimal trade-off between engine performance and emission reductions.

Engine performance tests revealed that the biodiesel blends delivered power outputs comparable to petroleum diesel. The B20 blend was particularly noteworthy, balancing performance and emissions. The elevated cetane number of the biodiesel blends contributed to an enhanced combustion efficiency; a critical factor for engine performance.

The environmental benefits of biodiesel blends were evident in the emissions analysis. The biodiesel blends resulted in reduced emissions of carbon monoxide (CO), hydrocarbons (HC), and particulate matter (PM) compared to petroleum diesel. However, an increase in nitrogen oxide (NO_x) emissions was observed, aligning with findings from other studies [1]. This indicates that while biodiesel offers substantial environmental advantages, further optimization is required to mitigate NO_x emissions.

Fuel consumption for the biodiesel blends was marginally higher than that of petroleum diesel, attributed to the lower calorific value of biodiesel. Despite this, the renewable nature and reduced environmental impact of biodiesel justify its use. The higher flash point of biodiesel also enhances its safety during storage and handling, making it a preferable option for various applications.

Utilizing WCO for biodiesel production addresses both waste disposal and fuel production challenges. This approach provides an economical and environmentally friendly solution, reducing dependency on fossil fuels and promoting sustainability. As demonstrated in this study, integrating advanced AI-driven decision-making frameworks can significantly improve the efficiency and sustainability of biodiesel production processes.

These findings have significant implications for policymakers and practitioners. Promoting biodiesel blends, particularly those derived from waste materials, can enhance national energy security and environmental sustainability. Policies supporting the collection and conversion of WCO to biodiesel can facilitate the adoption of cleaner energy solutions.

7. Conclusions and Future Work

This research aimed to identify the optimal mixture of cooking oils and diesel fuel available in the Egyptian market through a multi-criteria decision-making approach. It assessed eight different fuel mixtures, namely diesel, B5, B10, B20, B30, B50, B75, and B100, which differed in their proportions of diesel to biodiesel. The evaluation employed multiple criteria, including carbon monoxide, carbon dioxide, nitrogen oxides, hydrocarbons, particulate matter, engine performance, fuel efficiency, engine and tailpipe noise, and exhaust gas temperature. The assessment utilized a single-cylinder, constant-speed, direct-injection diesel engine with a 4.4 kW rated power under varied load conditions. This study applied grey relational analysis and the TOPSIS method to identify the most suitable fuel mixture. This combined GRA-TOPSIS approach facilitated the comprehensive ranking of the fuel alternatives. According to the findings, diesel emerged as the top fuel blend choice, followed by B5, B20, B10, B75, B30, B50, and B100.

The findings of this study underscore the potential of biodiesel derived from waste cooking oil (WCO) as a viable alternative to conventional diesel fuel. The evaluation framework, integrating grey relational analysis (GRA) with the technique for order preference by similarity to the ideal solution (TOPSIS), provided a robust framework for assessing the performances of the various biodiesel blends. The experimental results demonstrated that the blends with lower biodiesel contents, particularly B5 and B20, exhibited superior performance across multiple metrics, including engine power, emissions, and fuel consumption. The B5 blend, in particular, emerged as the optimal choice, balancing efficiency and emission reductions. These findings underscore the feasibility of using WCO-derived biodiesel as a viable alternative fuel, offering significant environmental and economic benefits.

This study also highlighted the elevated cetane number of the biodiesel blends, which improved the combustion efficiency and engine performance. While the biodiesel blends exhibitedreduced emissions of carbon monoxide (CO), hydrocarbons (HC), and particulate matter (PM), the increase in nitrogen oxides (NO_x) emissions warrants further optimization to enhance the overall environmental benefits of biodiesel. The higher flash point of biodiesel enhances its safety profile during storage and handling, making it a preferable option for various applications. Moreover, using WCO for biodiesel production addresses the dual challenges of waste disposal and sustainable fuel production, promoting a circular economy and reducing dependency on fossil fuels.

The implications of these findings for policymakers and practitioners are significant. Promoting biodiesel blends, particularly those derived from waste materials, can enhance national energy security and environmental sustainability. Policymaking efforts should focus on supporting the collection and conversion of WCO to biodiesel, facilitating the transition to cleaner energy solutions.

Future research should aim to optimize the biodiesel production process to further reduce NO_x emissions and improve fuel efficiency. Additionally, investigating the economic feasibility of large-scale biodiesel production from WCO in different regions will provide valuable insights for broader implementation. Looking ahead, similar multi-criteria decision-making methods can be employed to tackle more intricate evaluation challenges. Determining the optimal fuel blend remains an area ripe for further exploration. Future endeavors will also see the application of our proposed framework to a broader array of evaluation scenarios across different magnitudes.