An experimental approach varying piston geometry for optimization of diesel engine performance and emissions using prioritized clustering approach

Abstract

The world is currently grappling with a severe fuel crisis, driving the urgent search for sustainable and renewable alternatives. Biodiesel stands out as a viable green option due to its biodegradability and lower emissions. However, its global adoption remains limited, primarily due to high conversion costs and low yield. This study investigates the use of sulfonated graphene (SGR) as a catalyst to enhance biodiesel production efficiency. A Petter-AV1 single-cylinder diesel engine was used to evaluate performance (BTE, BSFC) and emissions (NOx, UBHC) through 14 experimental trials, with total uncertainty below 5%, confirming test reliability. Given the complex interactions among these parameters, stemming from nonlinear combustion behavior and physicochemical dependencies, a hybrid optimization method is applied, integrating Pearson-based priority analysis with k-means machine learning clustering. AHP–k-means is specifically selected due to its strength in addressing the multi-dimensional complexity of biodiesel properties. Its precision in prioritizing influencing factors and clustering performance-emission outcomes makes it ideal for optimizing biodiesel blends in diesel engine setup. Sulfonated graphene effectively enhances the transesterification process, achieving a high biodiesel yield of 94%. Nanoparticle concentration had the most significant effect, showing strong positive correlation with BTE (r = 0.6247) and strong negative correlation with BSFC (r = − 0.5802) and UBHC (r = − 0.6634), though it increased NOx (r = 0.6168). Among the input parameters, nanoparticle concentration held the highest priority (48%), followed by blend percentage (27%). The optimal trial (Trial 13) featured 40% biodiesel blend, 20 ppm NPC, 100% load, and a toroidal piston head, resulting in BTE of 42.30%, BSFC of 0.34 kJ/kWh, NOx at 620.18 ppm, and UBHC at 39.60 ppm. These findings highlight the promising role of SGR in improving biodiesel yield and its potential application in converting wastewater treatment plants into sustainable fuels.

Introduction

The world is currently facing a critical energy crisis as conventional fossil fuel reserves are depleting rapidly due to the growing global population and increasing energy demands¹. Fossil fuel combustion contributes heavily to greenhouse gas emissions, primarily CO₂ and NOₓ, which are major drivers of climate change and air pollution². Therefore, there is an urgent need to shift towards sustainable and cleaner fuel alternatives that not only reduce environmental impact but also ensure long-term energy security and public health protection^3,4. Biodiesel has emerged as a promising renewable alternative owing to its biodegradability, non-toxicity, and reduced emission profile. However, its widespread adoption is limited by high feedstock procurement costs, which require arable land and intensive farming inputs⁵. Moreover, the transesterification process used in biodiesel production often suffers from low conversion efficiency and requires expensive catalysts and energy inputs, leading to higher overall costs^6,7. Alternatively, utilizing invasive aquatic plants such as water hyacinth, which proliferate in wastewater and deplete dissolved oxygen offers a dual-benefit solution^8–10. These waste plants are abundantly available at no procurement cost and can be effectively converted into biodiesel feedstock¹¹. Enhancing the conversion process with advanced catalysts significantly improves reaction kinetics, thereby reducing reaction time, lowering energy consumption, and increasing biodiesel yield, making the process economically and environmentally viable^12–14.

Sulfonated graphene, with its expansive surface area and remarkable chemical reactivity, offers significant potential in biomass pretreatment, particularly by breaking down complex structural polymers such as lignin, cellulose, and hemicellulose¹⁵. When integrated into wastewater treatment systems, it demonstrates strong affinity toward these compounds, enhancing their degradation and removal¹⁶. This step is crucial, as these structural barriers typically hinder lipid extraction and downstream conversion, thereby limiting biodiesel yield¹⁷. Minimizing their presence streamlines the biomass-to-biodiesel pathway, boosting conversion efficiency and supporting a greener, resource-efficient energy production strategy¹⁸. Furthermore, hydrogen gas, when used synergistically with engineered nanoparticles, acts as a potent catalytic agent in biodiesel synthesis¹⁹. It actively accelerates transesterification reactions by facilitating the cleavage of ester linkages in triglycerides, improving the reaction’s rate and precision²⁰. This catalytic hydrogenation process not only speeds up biodiesel formation but also refines the final product by enhancing its oxidative stability and storage longevity²¹. Such advancements in catalyst technology contribute significantly to making biodiesel production more viable and industrially scalable²². However, the interdependencies among biodiesel yield and parameters like nanoparticle concentration and blend ratio, are highly nonlinear and intercorrelated, making conventional techniques insufficient for accurate optimization²³. A hybrid methodology is essential as it can handle multivariate complexity and uncover hidden patterns²⁴.

Recent research efforts have increasingly adopted advanced analytical techniques to evaluate and optimize engine performance, reflecting the evolving innovation in this domain²⁵. These studies have emphasized a thorough examination of decision-making criteria by assigning relative importance or weights to various performance and emission parameters²⁶. Methodologies such as the Analytic Hierarchy Process (AHP), entropy-based weighting, and equal weight distribution have been extensively used to quantify the influence of each factor^27,28. AHP provides structured pairwise comparisons to reflect expert judgment, contributing uniquely to a more accurate and balanced performance evaluation framework²⁹. Although the priority weights derived from methods are generally accurate, they often rely on subjective expert inputs, which may introduce bias or inconsistency³⁰. To overcome this limitation, integrating correlation analysis with a priority-setting technique enhances the objectivity by quantitatively identifying the strength of relationships between input parameters and biodiesel yield³¹. This hybrid approach ensures more reliable weight assignment by combining data-driven insights with structured prioritization³². The resulting weighted parameters are then fed into clustering algorithms, which group similar data patterns and isolate optimal operating conditions³³. In biodiesel research, where multiple interdependent variables influence yield and engine performance, this hybrid framework allows for more precise optimization, minimizing experimental trials while maximizing efficiency and output quality.

Nongbe et al.³⁴ investigated sulfonated graphene, synthesized via chemical exfoliation and benzene sulfonic acid functionalization, as a heterogeneous catalyst for palm oil transesterification with methanol. Achieved > 98% biodiesel purity under optimized conditions (methanol-to-oil ratio, temperature, time, catalyst loading), with high thermal stability and reusability without yield loss. Farid et al.³⁵ studied biomass-derived sulfonated graphene oxide catalysts (bGO-SO3H, brGO-SO3H) under microwave irradiation for biodiesel synthesis, confirming high acid density and sulfonation via thermal, titration, and spectroscopic analyses. Achieved up to 97.45% FAME yield at 1.5 wt%, 20:1 methanol ratio, 75 °C in 20 min, demonstrating enhanced efficiency with reduced catalyst and reaction time. Dos Santos et al.³⁶ developed sulfonic-reduced graphene oxide (rGO-SO3H) catalyst with high sulfonic group loading (12.1 ± 0.71 mmol g⁻¹) for soybean oil transesterification. Achieved 99% biodiesel yield with excellent recyclability over five cycles, attributed to stable C-SO₃H bonding and enhanced mass transfer. Hoseini et al.³⁷ explored the effect of graphene oxide (GO) nanoparticles (30–90 ppm) on B20 Oenothera lamarckiana biodiesel in a diesel engine at 2100 rpm. GO addition enhanced power and EGT, reduced CO (5–22%) and UHCs (17–26%), with slight increases in CO₂ (7–11%) and NOx (4–9%), suggesting GO as an effective additive. Gad et al.³⁸ studied B20 biodiesel from waste cooking oil enriched with 25–100 ppm CNTs and graphene nanosheets, using 2% surfactant for stability. B20CNS100 showed superior outcomes with 19% rise in efficiency, 54% smoke, 47% CO, 44% NOx, 52% HC reduction, and 22% lower ignition delay, recommending it as the optimal additive blend.

Within the existing body of literature, very few studies have explored biodiesel-diesel blends derived from wastewater plant biomass processed using sulfonated graphene oxide, primarily due to the complexity involved in its synthesis and catalytic application. This is attributed to precise control over reaction kinetics needed to effectively utilize sulfonated graphene oxide as a catalyst in heterogeneous biodiesel production systems. Moreover, performance and emission analysis of such produced biodiesel is extremely scarce in diesel engine-based studies. This study is motivated by the need to enhance biodiesel yield from low-cost wastewater plant feedstocks using efficient and sustainable catalytic methods. Leveraging sulfonated graphene and advanced hybrid optimization aims to overcome existing limitations in conversion efficiency and process scalability, along with improvements in performance and emission characteristics of diesel engine using these produced blends. The novelty of the study lies in utilizing wastewater-grown aquatic as a sustainable and abundant bio-resource for biodiesel production, addressing both energy generation and water pollution mitigation. This approach explores the untapped potential of invasive species, converting them into high-yield biofuel using sulfonated graphene catalyst in the presence of hydrogen. The application of a hybrid Pearson–AHP–k-means methodology further distinguishes the study by systematically prioritizing and clustering engine performance-emission outcomes.

The primary objective of this study is to produce biodiesel from water hyacinth biomass using sulfonated graphene and hydrogen gas as catalytic agents to enhance conversion efficiency. Following biodiesel synthesis, various biodiesel-diesel blends are tested in a diesel engine under different operating conditions to assess performance and emission characteristics. The experimental results are then subjected to Pearson inter-correlation analysis to identify the strength of relationships among input parameters. These correlation values are further utilized to derive parameter priorities using Analytic Hierarchy Process (AHP), providing a data-informed and structured weighting scheme. Finally, the prioritized parameters are applied within a k-means clustering model to group similar trial outcomes, enabling optimal combinations for maximizing engine performance and minimizing emissions.

Raw material selection and fuel preparation

In the initial phase of the study, biodiesel will be produced from water hyacinth, a waste-derived aquatic plant, using sulfonated graphene as a solid acid catalyst. The process comprises of biomass pretreatment, oil extraction, and a transesterification reaction catalyzed by SGR in presence of hydrogen gas, aimed at enhancing conversion efficiency. The quality and stability of the biodiesel-nano additive blend will be confirmed using SEM-TEM analyses to examine particle structure and crystallinity.

In the next phase, the produced biodiesel blends will be tested in a single-cylinder diesel engine to analyse key performance parameters and emission characteristics. The goal of engine testing is to evaluate the practical viability of the biodiesel blend and understand its effect on engine behavior. A hybrid data analysis approach will be employed, beginning with using Pearson correlation to determine interrelationships among engine parameters, followed by the AHP to prioritize the most influential factors. Finally, k-means clustering grouped experimental conditions that yielded the most favourable outcomes. This integrated methodology suits the complex and interdependent nature of biodiesel and diesel engine interactions.

raw material selection

The biodiesel production process from water hyacinth using an ultrasonic reactor requires specific set of materials to ensure efficient and effective operation. The water hyacinth, sourced from pond ecosystems as illustrated in Fig. 1, serves as the primary feedstock. Choosing waste aquatic plants like water hyacinth for biodiesel production addresses dual challenges of invasive species control and sustainable fuel sourcing. These plants are rich in lignocellulosic content, making them suitable for oil extraction and conversion via transesterification. Utilizing such biomass also reduces dependency on food-based feedstocks, promoting environmental and economic sustainability. If left uncontrolled, water hyacinth aggressively absorbs nutrients and water from aquatic bodies, leading to reduced water availability and oxygen depletion. This causes severe ecological imbalance, hindering marine biodiversity and water resource management. Essential components include water hyacinth oil, methanol as the alcohol reactant, and a catalyst. The ultrasonic reactor is equipped with a high-frequency transducer that generates mechanical vibrations which is central to the process. Additional equipment such as reactor vessels, mixing tanks, and heat sources are also necessary to maintain optimal reaction conditions. Together, these materials and devices create a controlled environment that supports a successful transesterification reaction, allowing for the efficient conversion of water hyacinth oil into high-quality biodiesel.

Fig. 1.

Water hyacinth collection site .

Among the various catalysts explored for biodiesel synthesis, graphene-based materials have attracted significant interest due to their high surface area and favourable functionalities¹⁵. However, in recent times sulfonated graphene has emerged as a particularly promising candidate owing to its enhanced catalytic performance in transesterification reactions. The incorporation of sulfonic acid groups (− SO₃H) into the graphene framework significantly increases the density of strong Brønsted acid sites, thereby facilitating faster and more efficient conversion of triglycerides into methyl esters. Additionally, SGR’s porous morphology and high surface reactivity ensure greater accessibility of reactants to catalytic sites, promoting improved mass transfer and reaction kinetics¹⁷. Its chemical and thermal stability also supports multiple cycles of reuse without significant activity loss, which is essential for sustainable and large-scale biodiesel production.

Compared to other graphene-based catalysts such as graphene oxide (GO), reduced graphene oxide (rGO), and metal-anchored graphene composites, SGR demonstrates several distinct advantages. While GO and rGO depend primarily on weaker oxygenated groups for catalysis and often degrade under reaction conditions, SGR offers robust acidity with minimal structural breakdown. Moreover, metal-supported graphene catalysts, although active, present challenges like metal leaching, environmental concerns, and higher production costs. SGR circumvents these issues with a cleaner, cost-effective synthesis method and strong acid functionality that enhances biodiesel yield and purity. These attributes not only distinguish SGR from conventional graphene catalysts but also establish it as a novel, scalable, and sound choice for advanced biodiesel production.

Hydrogen has emerged as a valuable reactant in transesterification processes due to its ability to facilitate cleaner, faster, and more energy-efficient chemical conversions. In biodiesel production, introducing hydrogen helps improve catalyst reactivity and promotes hydrogenation reactions that stabilize intermediate compounds. This enhances overall conversion efficiency and biodiesel yield. This enhances the reaction kinetics by lowering the activation energy barrier during transesterification, thereby promoting faster conversion of triglycerides to methyl esters, eventually increasing biodiesel yield. Its high reactivity accelerates intermediate breakdown and supports cleaner reaction pathways.

Fuel preparation analysis

Biodiesel production stands as a promising pathway to sustainable energy, and incorporating ultrasonic reactors introduces an innovative enhancement to the conventional production process, as shown in Fig. 2. To synthesize biodiesel from water hyacinth using sulfonated graphene as a catalyst, a multi-stage process is followed. Initially, water hyacinth biomass undergoes pre-treatment with 1% (w/w) sulfonated graphene at 150 °C for 2 h. This step reduces volatile matter and facilitates the breakdown of complex polymers like lignin and cellulose, improving the feedstock’s suitability for transesterification. During the transesterification process, hydrogen gas is introduced alongside methanol and the sulfonated graphene catalyst under ultrasonic agitation. Hydrogen plays a critical role by accelerating reaction kinetics through improved bond cleavage of triglyceride molecules. It also helps reduce activation energy, promotes ester bond dissociation, and prevents the formation of intermediate byproducts, leading to a cleaner and faster conversion.

Fig. 2.

Schematic diagram of biodiesel production and utilisation in Diesel engine .

The optimized reaction is maintained at 60 °C for 90 min under continuous ultrasonic waves (20 kHz) and a hydrogen flow rate of 0.5 L/min. After the reaction, the mixture is allowed to settle for 12 h in a separating funnel. The resulting biodiesel separates from the denser glycerine layer, which settles at the bottom. Typically, for every 100 mL of processed oil extracted from the biomass, approximately 85–90 mL of biodiesel and 10–15 mL of glycerine is obtained. The biodiesel is then washed with warm deionized water (at 50 °C) until neutral pH is achieved, followed by drying at 110 °C to remove residual moisture. This integrated process not only enhances biodiesel yield significantly but also demonstrates the synergy between hydrogen gas and sulfonated graphene in producing high-purity biofuel from waste biomass. The physiochemical properties of the produced biofuel are shown in Table1.

Table 1.

Comparison of physiochemical properties for produced fuels.

Properties	Biodiesel + SGR + H2	Biodiesel	Neat diesel	ASTM limit
Density at 15°C (kg/m3)	881	907	841	850–910
Kinematic viscosity (cSt)	3.55	2.77	4.56	2.52- 7.5
Calorific value (MJ/kg)	48.8	42.53	44.85	Min. 33
Flash point (°C)	73.56	110	51	Min. 130
Cetane number (⁰C)	57	53	51.3	Min. 45

Biodiesel blending procedure

The produced biodiesel from water hyacinth is blended with conventional petro-diesel in proportions of B10, B20, B30, and B40, where the numeric value indicates the percentage of biodiesel in the blend. These specific blend ratios are chosen to evaluate the progressive effect of biodiesel content on engine performance and emissions while ensuring compatibility with existing diesel engine systems. Lower blends like B10 and B20 allow minimal modification to engine settings, maintaining fuel injection properties close to conventional diesel, whereas higher blends like B30 and B40 are tested to examine the threshold at which efficiency varies. To further enhance the fuel properties, aluminium oxide nanoparticles are added at varying concentrations of 20 ppm, 40 ppm, 60 ppm, and 80 ppm. These concentrations are strategically selected to study the catalytic and thermal conductivity effects of nanoparticles on diesel engine. To counteract the tendency of biodiesel and nanoparticles to separate, a non-ionic surfactant Tween 80 is incorporated to enhance colloidal stability. The surfactant reduces interfacial tension and improves the dispersion of nanoparticles within the fuel matrix, ensuring uniform mixing and consistent fuel properties throughout engine operation.

Diesel engine experimental setup for performance and emission analysis

The experimental investigation was carried out on a single-cylinder, four-stroke, water-cooled Petter AV-1 diesel engine widely recognized for its robust design and suitability for variable fuel testing as shown in Table 2. The engine specifications include a rated power output of 5 HP at 1500 rpm, a bore and stroke of 80 mm × 110 mm, and a compression ratio of 17.5:1. The setup is equipped with a piezoelectric pressure sensor, crank angle encoder, and exhaust gas analyzer to capture real-time data on cylinder pressure and emissions. The engine was coupled to an eddy current dynamometer for applying variable loads and to record performance parameters such as BTE and BSFC under controlled conditions. Moreover, to assess the influence of combustion chamber geometry, four different piston head designs namely bowl, toroidal, re-entrant, and flat-head were tested. These variations aimed to study the swirl intensity and air–fuel mixing characteristics that directly affect combustion efficiency and emission formation. The engine was also operated at different loading conditions of 25%, 50%, 75%, and 100% of the rated capacity to simulate partial and full-load scenarios.

Table 2.

Specifications of the diesel engine used for performance and emission analysis.

Parameter	Specification
Engine model	Petter AV-1
Engine type	Single-cylinder, 4-stroke, CI
Cooling type	Water-cooled
Rated power	5 HP @ 1500 rpm
Bore × Stroke	80 mm × 110 mm
Compression ratio	17.5:1
Injection pressure range	190–220 bar
Fuel injection system	Direct injection
Dynamometer	Eddy current type

Uncertainty analysis for diesel engine parameters

In experimental engine testing, accurately assessing the performance and emission characteristics of alternative fuels like biodiesel is crucial for validating their practical applicability. Due to the inherent variability in engine behavior and measurement instruments, it becomes essential to quantify the associated uncertainties to ensure the credibility of the results. The uncertainty analysis was performed to quantify the reliability of performance (BTE, BSFC) and emission (UBHC, NOx) parameters measured from the diesel engine tests using biodiesel blends as shown in Table 3. For each parameter, the Type A uncertainty (statistical variation across multiple test runs) and Type B uncertainty (instrumental or calibration errors) were calculated and combined using the root-sum-square method. This combined uncertainty was then expressed as a percentage of the measured value. The total uncertainty for all key parameters was found to be less than 5%, confirming that the experimental results are statistically robust and within acceptable error margins, thereby validating the consistency and reliability of the biodiesel testing process.

Table 3.

Instrument accuracies for key parameters.

Parameter	Measured using	Instrument accuracy ( ±)	Uncertainty
BTE	Fuel flow sensor, torque meter, speed sensor	Fuel flow: 0.5%, Torque: 0.3%, Speed: 0.1%, Calorific value: 0.2%	± 0.62
BSFC	Fuel flow sensor, brake power measurement	Fuel flow: 0.5%, Torque: 0.3%, Speed: 0.1%	± 0.59
UBHC	Gas analyzer	± 1.0%	± 1.0%
Nox	Gas analyzer	± 1.0%	± 1.0%

Methodology

The complex interactions among engine inputs and outcomes necessitate a robust hybrid methodology capable of capturing nonlinear dependencies and optimizing multidimensional parameters effectively. The prepared biodiesel blends derived from water hyacinth are tested in a single-cylinder diesel engine to evaluate performance parameters (BTE and BSFC), along with emission characteristics (NOx and UBHC) as shown in Fig. 3. The obtained results are then subjected to Pearson-r correlation analysis to determine the interrelationship between input variables and engine outcomes. These correlations are subsequently used in AHP to assign priority weights to each input parameter based on their influence on performance and emissions. The prioritized variables are then clustered using the K-means clustering algorithm, facilitating optimization by identifying the most suitable input combinations for achieving ideal engine performance and reduced emissions.

Fig. 3.

Representation of the hybrid optimization methodology.

Diesel engine outcomes and their evaluation process

The evaluation of outcome parameters along with their formulas is provided below, and the corresponding experimental results are presented in Table 4. The measurement of BTE together with BSFC enables effective assessment of biodiesel energy performance proving biodiesels dominance over other fuels. The outcome emission measures of UBHC, and NOx assist in designing fuel systems because they balance emissions and structural integrity. The following are the outcomes considered for the study:

Table 4.

Experimental performance and emission outcomes for diesel engine.

Exp. No	B (%)	NPC (ppm)	LD (%)	Piston head	BTE (%)	BSFC (kJ/kWh)	NOx (ppm)	UBHC (ppm)
1	10	20	25	Flat	29.85	0.47	868.10	49.65
2	10	40	50	Bowl	34.05	0.37	698.72	40.28
3	10	60	75	Toroidal	36.65	0.36	720.44	39.71
4	10	80	100	Re-entrant	38.90	0.34	709.55	38.10
5	20	20	50	Flat	32.15	0.44	851.40	47.12
6	20	40	25	Bowl	36.85	0.41	805.33	43.55
7	20	60	100	Toroidal	37.10	0.36	675.24	39.92
8	20	80	75	Re-entrant	40.25	0.34	638.18	36.40
9	30	20	75	Flat	33.05	0.45	860.60	47.34
10	30	40	100	Bowl	35.85	0.38	812.12	40.87
11	30	60	25	Flat	38.10	0.37	710.20	38.55
12	30	80	50	Re-entrant	42.00	0.33	675.77	35.20
13	40	20	100	Toroidal	42.30	0.34	620.18	39.60
14	40	40	75	Bowl	35.65	0.39	755.42	40.75

1. Brake Thermal Efficiency (BTE, %) Ratio of useful engine power output to the fuel energy input, indicating how efficiently the engine converts fuel into work.

1

where:

• (kW, : engine speed [rpm], : torque [Nm])

• : Fuel mass flow rate [kg/s]

• : Lower heating value of fuel [kJ/kg].

2. Brake-Specific Fuel Consumption (BSFC, kJ/kWh) Fuel consumption rate per unit of power output, showing how much fuel is needed to produce one kilowatt-hour of energy.

2

3. Unburned Hydrocarbons (UBHC, ppm) Measure of hydrocarbons that escape combustion, indicating incomplete fuel burning and contributing to emissions.

3

where:

• : Volumetric concentration of HC [%]

• : Exhaust flow rate [m³/s]

• : Exhaust gas density [kg/m³]

• : Molar mass of hydrocarbons [g/mol].

4. Nitrogen Oxides (NOx, ppm) Harmful emissions formed at high temperatures during combustion, primarily nitrogen monoxide (NO) and nitrogen dioxide (NO₂).

4

where (ideal gas law, : pressure [Pa], : temperature [K], : gas constant).

Selecting appropriate engine operating parameters is also crucial for accurately assessing the impact of biodiesel blends on diesel engine performance and emissions as shown in Table 4. Variations in blend ratio, nano-additive concentration, load, and piston head design significantly influence combustion efficiency, fuel utilization, and pollutant formation. The biodiesel blend levels—10%, 20%, 30%, and 40%—are chosen based on the typical blending ranges where performance transitions are evident without requiring engine modifications³⁹. Below 10%, the influence of biodiesel is marginal, while above 40%, issues like increased viscosity, injector clogging, and delayed combustion may emerge. Similarly, the nano-particle concentration levels of 20, 40, 60, and 80 ppm are set within a safe operational threshold that ensures improved atomization and catalytic activity without causing nanoparticle agglomeration or wear in the engine parts⁴⁰. Beyond 80 ppm, particles tend to settle or interfere with spray dynamics, reducing combustion quality. These combinations help isolate the effect of each parameter in a controlled manner while maximizing engine output and emissions reduction⁴¹.

For the load condition, four levels—25%, 50%, 75%, and 100%—were selected to simulate realistic engine operating scenarios, ranging from low to full load. Very low or idle loads are typically unstable for accurate emission measurement, while 100% load marks peak combustion conditions⁴². Regarding piston head geometry (Flat, Bowl, Toroidal, and Re-entrant), each shape induces distinct air–fuel mixing characteristics and turbulence levels. This affects swirl, squish, and flame propagation, all of which influence combustion completeness and emission formation⁴³. These selected geometries represent practical engine design variations and offer insights into how chamber shape alters biodiesel–air interaction. Overall, all these parameters are highly relevant and interdependent in determining diesel engine performance and emissions in biodiesel testing⁴⁴.

Pearson-r based correlation analysis

Pearson-r correlation analysis is a highly effective statistical tool for examining complex interaction processes that involve diverse physicochemical properties of alternative fuels and nano-additives. In such multi-variable systems, where each input can influence multiple performance and emission outcomes differently, Pearson-r helps quantify the linear relationship strength between each input parameter and outcome. Based on the computed Pearson-r and R² values, correlations are categorized as weak, moderate, or strong, enabling a systematic understanding of the influence pattern. These insights are critical for rational decision-making and are further utilized in the AHP model, where the established correlation strengths serve as a basis to assign priority weights to each input variable, thereby supporting a structured and unbiased approach for optimizing biodiesel engine performance.

The Pearson-r correlation coefficient is calculated using the following equation:

5

where:

• r = Pearson correlation coefficient

• n = Number of data pairs

• x, y = Individual sample points

• ∑xy = Sum of the product of paired scores

• ∑x, ∑y = Sum of x scores and y scores respectively

• ∑x², ∑y² = Sum of squares of x and y scores

AHP-k-means clustering optimisation method

After obtaining the inter-correlation results between input variables and engine performance-emission outcomes using Pearson-r analysis, these values are used as inputs for the Fuzzy Analytic Hierarchy Process (Fuzzy AHP) to establish the priority of each parameter. Fuzzy AHP calculates the relative weights of input parameters by incorporating the uncertainty and vagueness inherent in complex decision-making through fuzzy logic, enabling more robust and improved prioritization. A consistency check is then performed to ensure reliable judgments, refining comparisons if necessary. After deriving priority weights, AHP aggregates them to rank alternatives or fuel combinations. These weights guide the clustering process or optimization model to focus on outcomes with higher priorities. Unlike traditional AHP, which relies on subjective judgments from human decision-makers and may introduce bias or inconsistency, Fuzzy AHP leverages correlation-based values grounded in experimental data, leading to a more objective, data-driven ranking. This makes it particularly suitable for optimization tasks in biodiesel-diesel blend systems.

The k-means clustering model optimizes diesel engine results by grouping similar data points, which helps identify the most effective fuel combinations and operational parameters for performance and emission outcomes. Unlike other optimization models, k-means is an unsupervised algorithm that can handle large datasets with multiple variables. It categorizes data into clusters based on similarity, which simplifies decision-making by highlighting the best, worst, and average conditions without requiring explicit labels or prior knowledge. This approach offers clear insights into which operational configurations lead to optimal engine performance, making it ideal for handling the complex, multidimensional data typically seen in diesel engine tests. k-means works by partitioning a dataset into 'k' clusters, where each cluster contains data points that are more similar to each other than to those in other clusters. The algorithm begins by selecting 'k' initial centroids and assigns data points to the nearest centroid. Then, the centroids are recalculated as the average of the points in each cluster. The process repeats until the centroids no longer change significantly. By iterating this process, k-means finds natural groupings within the data, which helps researchers identify trends and optimize parameters based on the most common or ideal outcomes.

Results and discussion

Catalyst preparation and characterization

SEM and XRD analytical methods are frequently utilized for classifying various nano additives. The SGR additives’ average particle size and nanostructure are analysed by microscopic electron scanning as shown in Fig. 4. The SEM image of the SGR nano additives is captured at a high resolution of 10,000 pixels. The particle size distribution was found to be uniform, with an average particle size ranging between 40–60 nm, indicating nanoscale consistency essential for stable fuel blends. The uniform dispersion quality observed across the surface suggests effective mixing and minimal agglomeration. Complementing this, TEM imaging reveals a transparent, crumpled graphene structure, confirming the successful exfoliation of graphene layers. This crinkled, paper-like morphology facilitates better surface area and interaction with the biofuel matrix, which is critical for improved combustion behavior and catalytic activity in the diesel engine. XRD analysis is utilized not only to determine the composition and crystalline arrangement of SGR nano additives but also to identify their constituent fragments and assess the degree of crystallinity. The XRD patterns of these nano additives were obtained using a X-ray diffractometer (λ = 1.56 Å) within the 2θ range of 300–1000, as depicted in Fig. 4. The quantity of SGR nano additives dispersed in the ECO30 standard fuel blend is contingent upon the volume of nano additives introduced. Furthermore, the diffusion of SGR nano additives was analysed using an ultraviolet spectrometer with a wavelength spectrum ranging from 200 to 1100 nm, maintaining a precise threshold of ± 0.3 nm.

Fig. 4.

SEM and XRD image of the SGR nano-additive.

Biodiesel yield enhancement

When SGR and hydrogen gas is introduced into the biodiesel production process, it acts as a catalyst, accelerating the breaking of complex matter into more accessible compounds. This breakdown leads to a greater availability of sugars and other organic materials that serve as precursors for biodiesel production. As a result, the biodiesel yield experiences a remarkable improvement, soaring from 58 ± 1.3 to 94 ± 1.3%. Figure 5 provides the fatty acid composition of EC oil and their respective weight percentages. The biodiesel was obtained in high purity (> 94%) and mainly consisted of oleate, palmitate, linoleate and stearate Palmitic acid (16:0) constitutes approximately 24.21% of the oil, followed by oleic acid (18:1) at 54.25%, which is the dominant fatty acid in the composition. Other fatty acids present include stearic acid (18:0) at 7.21%, linoleic acid (18:2) at 11.31%, arachidate (C20:0) at 2.04%, and eicosenate (C20:1) at 0.99%. The use of sulfonated graphene nanoparticles (SGNPs) in biodiesel production significantly enhances the transesterification process, ensuring the fatty acid composition meets optimal targets for diesel engine compatibility. The achieved values for palmitic (16:0), stearic (18:0), oleic (18:1), linoleic (18:2), arachidate (C20:0), and eicosenate (C20:1) closely align with their target values due to the catalytic efficiency of SGNPs. This is attributed to the nanoparticles’ high surface area, uniform sulfonic acid sites, and excellent thermal stability, enabling superior conversion of feedstock into biodiesel with balanced fatty acid profiles. The achieved value of oleic acid (54.25%) is nearly identical to the target (54.5%), ensuring the fuel’s oxidative stability and combustion efficiency. The specific values indicate that the biodiesel produced is “Good” across all fatty acid compositions, highlighting SGNPs’ role in fine-tuning these parameters. The slightly higher oleic acid content (54.25%) ensures excellent lubricity and reduced NOx emissions, while moderate levels of palmitic (24.21%) and stearic acid (7.21%) enhance cetane number and cold flow properties. Linoleic acid (11.31%) remains within a safe range to maintain oxidative stability, crucial for engine performance. Similarly, low levels of arachidate (2.04%) and eicosenate (0.99%) prevent polymerization issues, confirming that the biodiesel is well-suited for diesel engines with minimal deposits and improved efficiency.

Fig. 5.

Comparison of fatty acid proportions for different value.

The confidence interval analysis demonstrates the statistical reliability of the biodiesel yield improvement process as shown in Table 5. Initially, the mean yield was 58.0% with a standard deviation of 1.3%, and after the use of hydrogen and SGR catalyst, the yield increased to 94.0% with the same standard deviation. With the same sample size, the calculated standard error (SE) is 0.41%, leading to 95% confidence intervals of 57.18–58.82% before and 93.18–94.82% after the intervention. The non-overlapping confidence intervals confirm a statistically significant improvement in biodiesel yield, reinforcing the effectiveness of the applied enhancement methodology and establishing the reliability of the experimental results.

Table 5.

Confidence interval analysis of biodiesel yield.

Biodiesel condition	Mean yield (%)	SD (%)	N	SE (%)	95% CI range (%)
Without SGR use	58.0	1.3	14	0.41	57.18–58.82
With SGR use	94.0	1.3	14	0.41	93.18–94.82

Pearson-r correlation analysis

In a recent diesel engine experiment, researchers conducted an analysis to understand the relationships between various input and output parameters, with a focus on key performance indicators as shown in Fig. 6. BTE shows a strong positive correlation with NPC (r = 0.6247) and a moderate positive correlation with Load (r = 0.3196), indicating that higher nanoparticle concentration and increased load improve combustion efficiency. The correlation with Blend % is weak (r = 0.0718), suggesting that blend ratio alone does not significantly influence thermal efficiency unless supported by other factors like catalysts or loading conditions. BSFC has a strong negative correlation with BTE (r = − 0.8918) and NPC (r = − 0.5802), indicating that better combustion efficiency and the presence of nanoparticles help reduce fuel consumption. The correlation with Load is moderate and negative (r = − 0.4638), showing that BSFC decreases with increased load to some extent. However, the correlation with Blend % is weak (r = − 0.1282), implying minor influence of blend alone on BSFC.

Fig. 6.

Pearson correlation map of diesel engine parameters.

NOx emissions show a very strong positive correlation with BSFC (r = 0.9207) and a moderate positive correlation with NPC (r = 0.6168), implying that better atomization and oxygen availability due to nanoparticles can increase combustion temperature and thus NOx. Load has a moderate correlation (r = 0.666), while Blend % shows negligible correlation (r = − 0.1373), indicating blend composition is not a dominant factor in NOx formation. UBHC emissions show a very strong negative correlation with BTE (r = − 0.8574) and strong negative correlation with NPC (r = − 0.6634), suggesting that better combustion through nanoparticles leads to more complete fuel burning. The correlation with Load is weak to moderate (r = − 0.4185), and with Blend %, it is weak (r = − 0.1691), reflecting minimal direct influence of these parameters on UBHC compared to BTE and NPC. These relationships emphasize that nanoparticle concentration and blending process play significant roles in influencing engine performance and emissions.

Weightage and ranking analysis

The Fig. 7 presents the range of different input parameter by AHP weightage process. This reflects the relative importance of each outcome based on various factors. The priority scores indicate that nanoparticle concentration (NPC) holds the highest priority at 48%, followed by blend percentage (B) at 27%, load (LD) at 15%, and piston-head design (PD) at 10%. This ranking suggests that the concentration of nanoparticles plays a dominant role in enhancing combustion efficiency, improving atomization, and promoting catalytic oxidation during biodiesel-diesel engine operation. Nanoparticles facilitate better air–fuel mixing and provide more active sites for reaction, which significantly influences both performance and emission metrics. The blend percentage ranks second, as the biodiesel content affects the oxygen availability and combustion temperature due to its intrinsic properties such as higher cetane number and oxygen content. However, its influence is comparatively lower than NPC because excessive biodiesel can increase viscosity and affect spray characteristics. Load and PD have lower priority scores since they are more secondary or situational parameters; while they do influence combustion behavior, their effects are not as pronounced or consistent across biodiesel-based experiments. Thus, optimizing NPC and blend ratio is more critical for achieving balanced performance and emissions in biodiesel-fueled engines.

Fig. 7.

Priority weightage analysis for operating parameters.

k-means machine learning clustering based optimisation analysis

K-means clustering offers powerful optimization by grouping data into well-defined clusters based on similarity, effectively reducing internal variation while enhancing the distinction between groups. Compared to other techniques, it handles large, high-dimensional datasets more efficiently, offering speed and scalability. Through repeated updates of cluster centroids, it converges toward optimal groupings, ideal for fine-tuning variables such as diesel engine performance and emission outputs. Its flexibility allows it to adapt to evolving input–output patterns, making it highly suitable for performance optimization in machine learning tasks.

Using a weighted AHP method, the k-means clustering process was refined to generate new final cluster centers, as shown in Table 6, which outperformed the initial cluster centers. The AHP model assigned optimized weights to each metric based on their relative importance, leading to better-defined clusters with improved parameter alignment. Table 6 presents the initial and final cluster centers (created after priority assignment). The clustering improves significantly when priority-based weighting is applied during the final clustering stage, as evident from the performance and emission values. In the initial clustering, Cluster 2 already had the highest BTE (42.30%) and lowest BSFC (0.34 kJ/kWh), but the remaining clusters showed more scattered performance. After incorporating priority—especially emphasizing parameters like BTE and BSFC, UBHC the final clusters become more compact and balanced. Also, the final Cluster 2 still maintains top efficiency (BTE: 40.41%) and minimal BSFC (0.34), while NOx and UBHC also improve to 652.34 ppm and 37.78 ppm, respectively, indicating that clustering refined by priority aligns better with desired engine outcomes and reduces variance in key indicators. This improvement highlights the dominance of machine learning models like AHP in optimizing clustering results by ensuring that clusters align with real-world performance.

Table 6.

Initial and final cluster center.

Initial cluster
	BTE	BSFC	Nox	UBHC
Cluster 1	29.85	0.47	868.1	49.65
Cluster 2	42.30	0.34	620.18	39.6
Cluster 3	35.65	0.39	755.42	40.75
Final cluster
Cluster 1	33.55	0.43	839.51	45.71
Cluster 2	40.41	0.34	652.34	37.78
Cluster 3	36.67	0.36	718.86	39.47

The cluster summary in Table 7 demonstrates the effectiveness of the machine learning algorithm in forming well-defined clusters. Cluster 3, with the lowest WCSS (1926.42) and the smallest average distance (15.40), indicates high cohesion and minimal variation among its observations, suggesting it represents the most stable group in terms of engine performance and emissions. Cluster 2, although having fewer observations (4), maintains a low WCSS (2341.68) and average distance (23.34), reflecting good homogeneity. Cluster 1, with higher WCSS (3402.37) and average distance (24.92), is slightly more dispersed but still within acceptable clustering range. The clustering distribution aligns well with technical expectations, proving the effectiveness of priority-based input consideration in grouping similar engine behavior patterns.

Table 7.

Cluster compactness and separation analysis.

	Number of observations	Within cluster sum of square	Average distance	Maximum distance
Cluster 1	5	3402.37	24.92	34.41
Cluster 2	4	2341.68	23.34	32.27
Cluster 3	5	1926.42	15.40	36.60

Figure 8 clearly demonstrates that each cluster is distinctly separated from the others, confirming the robustness of the clustering process and the reliability of the selected dataset. The inter-cluster distances—120.84 (Cluster 1 vs. 3), 187.46 (Cluster 1 vs. 2), and 66.65 (Cluster 2 vs. 3)—highlight significant dissimilarities in performance-emission characteristics. The highest distance between Cluster 1 (Worst) and Cluster 2 (Best) reinforces their contrasting behavior, while even the closest pair (Clusters 2 and 3) maintain a meaningful separation. This validates that the clusters are well-formed and non-overlapping, technically affirming the quality and discriminative strength of the input parameters used.

Fig. 8.

Heat-map analysis for different clusters.

The Table 8 highlights the centroidal distances of data points from their respective cluster centers, with the best cluster identified as having the lowest distance to the centroid. Data point 13, with a centroidal distance of 5.78, stands out as the closest to the optimal cluster center, aligning with its principal component scores (PC1: -2.17, PC2: 0.34) as shown in Fig. 9. This proximity signifies its robust alignment with the “Best” cluster type, which is characterized by high efficiency and favorable emission outcomes. The technical attributes of Data 13—fuel blend (B-40, NPC-20), high load (100%), and injection pressure (200 bar)—drive its exceptional results, including a superior BTE of 42.30%, minimal BSFC of 0.34(kJ/kWh), reduced NOx emissions at 620.18 ppm, and controlled UBHC at 39.60 ppm.

Table 8.

Principal component scores for each cluster.

S No	Relationship	Distance	PC-1	PC-2	Group classification
1	1	29.09	3.68	− 0.20	Worst
2	3	20.33	− 0.16	− 0.94	Average
3	3	1.59	− 0.57	− 0.26	Average
4	3	9.67	− 1.37	0.06	Average
5	1	12.05	2.62	0.03	Worst
6	1	34.41	0.94	0.61	Worst
7	2	23.23	− 0.87	− 0.43	Best
8	2	32.95	− 2.17	− 0.11	Best
9	1	21.16	2.69	0.35	Worst
10	1	27.91	0.45	0.23	Worst
11	3	8.83	− 0.85	0.01	Average
12	2	23.62	− 2.44	0.43	Best
13	2	14.23	− 2.17	0.34	Best
14	3	36.60	0.24	− 0.13	Average

Fig. 9.

Principal components score for all clusters.

Data point 13 exhibits the smallest centroidal distance of 5.78, indicating its strong alignment with the optimal cluster and confirming it as the most representative configuration within that group as shown in Fig. 9. The superior performance of Data 13 is attributed to its balanced input parameters and outcomes. The B-40 blend, enriched with nanoparticles (NPC-20), enhances combustion efficiency due to better atomization and improved energy release, reflected in its high BTE. The optimized toroidal head design promotes better mixing of air and fuel, reducing BSFC and limiting incomplete combustion, as evident from its low UBHC values. Additionally, the reduced NOx emissions (632.75 ppm) demonstrate effective thermal management under high load conditions, showcasing the synergistic impact of its well-calibrated inputs. These justifications establish Data 13 as the most effective dataset for optimal diesel engine performance with minimal emissions.

The ANOVA analysis underscored essential aspects such as central tendency, variability, and significant differences among variables across various clusters, as shown in Table 9. The ANOVA results, reflect the effectiveness of the k-means clustering algorithm in analyzing key performance (BTE, BSFC) and emission (NOx, UBHC) metrics for biodiesel-fueled diesel engines. The clustering process was conducted to group data points based on similar characteristics, helping to identify patterns in engine performance and emission outcomes. The mean and standard deviation values indicate the central tendency and variation of the metrics within each cluster, while the F-value and Prob > F highlight the significance of the differences between clusters. The ANOVA analysis statistically validate the accuracy of the clustering optimization process. The high F-values for all outcomes—particularly NOx (F = 60.10) and BSFC (F = 15.41)—combined with very low p-values (all < 0.005), confirm that the variation between clusters is statistically significant and not due to random chance. This demonstrates that the clusters formed differ meaningfully in terms of BTE, BSFC, NOx, and UBHC, thereby justifying the robustness and reliability of the clustering-based optimization approach used in the study.

Table 9.

ANOVA results for k-means clustering.

Outcome	Mean	Standard deviation	F-Value	Prob > F
BTE	36.62	3.60	8.98	0.00487
BSFC	0.38	0.04	15.41	6.45401E-4
NOx	742.94	83.15	60.10	< 0.0001
UBHC	41.21	4.23	12.85	0.00132

Discussion

The influence of operational parameters, on BTE can be profound as shown in Fig. 10. BTE generally improves with increases in nanoparticle concentration, biodiesel blend percentage (B), and load (LD), provided these parameters are optimized. However, higher nanoparticle concentration can also be detrimental to diesel engine resulting in frequent valve clogging. Optimum NPC range boosts the combustion through catalytic activity of nanoparticles, while a higher load improves fuel utilization. Hence, increasing NPC to a certain range boosts atomization and oxygen availability, promoting more complete combustion and reducing heat losses, which positively impacts BTE⁴⁵. Furthermore, the blend percentage also contributes significantly, indicating the synergistic effect of load and oxygenated fuel content improving combustion characteristics⁴⁶. Thus, the interplay of these variables must be carefully balanced to maximize efficiency in diesel engines running on biodiesel-nanoparticle blends.

Fig. 10.

Impact of operating parameters on BTE (Plotted by Design Experiment version 12).

The interplay of operational parameters, can significantly impact BSFC as shown in Fig. 11. The BSFC demonstrates a decreasing trend with an increase in NPC, blend percentage, and load, signifying improved combustion efficiency. This is due to better fuel atomization and catalytic action of nanoparticles, which enhance combustion and reduce unburnt fuel losses⁴⁷. Higher loads also contribute to lower BSFC, as engines operate closer to their optimal efficiency range with reduced relative friction and thermal losses. However, at sub-optimal combinations, such as low LD, BSFC remains higher due to incomplete combustion and higher fuel demand to maintain engine output. Although biodiesel has a lower calorific value than diesel, its oxygen-rich nature supports cleaner burning when properly assisted by nanoparticles⁴⁸. Thus, the data confirms that a balanced increase in NPC, B, and LD leads to more efficient fuel use, reducing BSFC significantly in biodiesel-powered diesel engines.

Fig. 11.

Impact of operating parameters on BSFC (Plotted by Design Experiment version 12).

The effects of operational parameters on NOx emissions are notable as shown in Fig. 12. The NOx emissions in the dataset show a general decreasing trend with an increase in NPC and load, especially when paired with higher biodiesel blend percentages. This reduction occurs because the improved combustion efficiency due to higher loads and catalytic action of nanoparticles allows better thermal distribution, reducing localized high-temperature zones that typically form NOx⁴⁹. Though biodiesel inherently promotes NOx formation due to its oxygen-rich nature and higher combustion temperatures, the presence of nanoparticles improves the combustion pattern, enabling shorter ignition delays and more uniform combustion. Additionally, higher load increases fuel utilization but lowers the oxygen-to-fuel ratio, limiting the excess oxygen available to form NOx. Thus, the synergy of biodiesel blending, effective nanoparticle dosing, and higher engine load optimizes combustion and suppresses NOx emissions.

Fig. 12.

Impact of operating parameters on NOx (Plotted by Design Experiment version 12).

The impact of operational parameters on UBHC emissions is significant as shown in Fig. 13. UBHC emissions consistently decline with optimum nanoparticle concentration, biodiesel blend percentage (B), and engine load (LD). This trend indicates more complete combustion due to improved atomization and catalytic effects of nanoparticles, which reduce unburnt hydrocarbon residues. Higher blends of biodiesel, being oxygenated, promote cleaner combustion and enhance BTE, thereby lowering UBHC formation. This improvement arises because biodiesel provides additional oxygen during combustion, and higher load increases in-cylinder temperature and pressure, aiding full fuel oxidation⁵⁰. Nanoparticles further reduce ignition delay and stabilize flame propagation, leading to better combustion efficiency and a notable decrease in UBHC emissions. Hence, the interplay of higher biodiesel content, efficient nanoparticle dispersion, and elevated load contributes to enhanced BTE and reduced UBHC.

Fig. 13.

Impact of operating parameters on UBHC (Plotted by Design Experiment version 12).

Conclusion

The current study introduces a novel biofuel derived from the invasive aquatic plant Water Hyacinth, converting its biomass into biodiesel for use in diesel engines. This process utilizes sulfonated graphene as an efficient catalyst due to its high surface area, strong acidic functional groups, and excellent thermal stability, which promote the breakdown of lignocellulosic structures. Extensive research was conducted to understand SGR’s catalytic activity and transesterification process. Furthermore, hydrogen gas is introduced during the conversion process to enhance reaction kinetics and improve the transesterification efficiency. The combined action of SGR and hydrogen significantly improves biodiesel yield, with the core objective of developing a sustainable, low-cost, and high-efficiency biofuel alternative from wastewater plants’ biomass. The biodiesel produced is tested in diesel engine. Performance outcomes BTE and BSFC were recorded, while emission parameters including NOx and UBHC were also measured to assess environmental impact.

Owing to the complex interactions between diesel engine performance and emission outcomes and various operating parameters, a hybrid analytical methodology is employed. Initially, Pearson correlation analysis is applied to quantify the strength and direction of relationships between input variables and output responses. These correlation values were then fed into a F-AHP, which effectively prioritized input variables based on their influence, overcoming the subjectivity and inconsistency of expert-based decision-making. Finally, K-means clustering was utilized to group similar experimental conditions and identify optimal clusters for enhanced performance and reduced emissions, enabling data-driven tuning of engine operating parameters. AHP–k-means was specifically chosen for its ability to handle the multi-dimensional complexity of biodiesel properties. Its accuracy in ranking critical input factors and clustering performance-emission results makes it highly suitable for optimizing biodiesel blends in diesel engine setups. The following conclusions were achieved from the study:

• Sulfonated graphene boosts the transesterification reaction resulting in high yield (94%) of biodiesel.

• A Petter-AV1 single-cylinder diesel engine is employed for performance (BTE and BSFC) and emission (NOx, and UBHC) analysis, comprising of 14 experimental trial runs.

• The total uncertainty for all key parameters remained below 5%, confirming the statistical reliability and consistency of the biodiesel engine testing process.

• Nanoparticle concentration shows strong positive influence on BTE (r = 0.6247) and strong negative correlation with BSFC (r = − 0.5802) and UBHC (r = − 0.6634), while NOx rises with NPC (r = 0.6168).

• With 48% priority achieved, the nano particle concentration (NPC) emerged as the most influential factor, followed by blend percentage (27%).

• The optimal input–outcome setting came out to be trial 13 with blend percentage of 40%, NPC 20 ppm, load: 100%, piston head type toroidal, achieving BTE: 42.30%, BSFC: 0.34 kJ/kWh, NOx: 620.18 ppm, and UBHC: 39.60 ppm.

The present study holds significant promise for real-world application due to its emphasis on a widely available aquatic weed as a potential bio-resource. Moreover, the biodiesel production process capitalizes on a low-cost, renewable feedstock, helping to reduce environmental burden and waste management issues, thereby confirming its economic viability. The addition of SGR nano additives not only enhances the physio-chemical properties of the biodiesel but also supports higher fuel yields and improved combustion, thus offsetting costs with performance gains. These nano additives, owing to their high dispersion stability and favourable surface properties, ensure uniform blending without causing injector clogging or deposition, which are common challenges in biodiesel usage. Importantly, the biodiesel blend demonstrates favourable compatibility with conventional diesel engines, requiring no significant changes to the engine hardware or fuel supply systems. This compatibility ensures ease of adoption in current transport or industrial systems, making the transition to greener fuels practically feasible. The methodology’s reliance on scalable synthesis techniques like transesterification and nano-additive dispersion using widely available laboratory equipment further strengthens the case for commercialization, demonstrating improved scalability. Overall, the study offers a balanced pathway toward sustainable, economically feasible biofuel solutions that can be integrated into the existing fuel economy with minimal disruption. The possible limitation of the study is its analysis was only performed in a single-cylinder diesel car engine testing, which may not fully represent marine or other large commercial engine performance. Additionally, long-term durability and storage stability of the water hyacinth-based biodiesel needs to be addressed for understanding its complete potential. Future studies can explore multi-cylinder and real-world engine testing to validate performance and emission outcomes. Long-term evaluation of biodiesel stability, material compatibility, and engine wear can further strengthen its practical applicability.

Author contributions

S.A. and Z.A. wrote the main manuscript text. M.Z.K. prepared all the figures. A.A. and H.H. conducted experimental analysis. M.J.I. and W.T. revised the manuscript. All authors reviewed the manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interest

The authors declare that there is no conflict of interests regarding publication of this manuscript.