Two-Stage Optimization of Oleic Acid Esterification via Response Surface Methodology and Green Chemistry Metrics Selection for Biodiesel from WCO

Abstract

Biodiesel production from used cooking oil (WCO) is a sustainable alternative to fossil fuels, but its high free fatty acid (FFA) content (>5 wt %) makes direct basic transesterification difficult. This study presents an integrated two-stage strategy that optimizes the acid esterification of oleic acid (the dominant FFA in WCO) using response surface methodology (RSM, Box–Behnken) and then evaluates downstream transesterification, while reporting green chemistry metrics alongside conversion. The RSM model identified an optimum at a methanol-to-oleic acid ratio of 8.44:1, 2 wt % H₂SO₄, and 363 min. Kinetic validation showed that conversion reaches ∼94% within 90 min and then plateaus, indicating a practical endpoint that reduces energy and time with minimal yield loss. Applied to a WCO feed (8.12 wt % FFA), the pretreatment reduced FFA to ∼2.4 wt %, enabling transesterification of the base to ∼98 wt % FAME with <0.5 wt % residual FFA. The final biodiesel met ASTM D6751 and EN 14214 specifications and exhibited a favorable FAME profile (∼75.6% methyl oleate). Green chemistry analysis clarified the trade-offs of these results, with the esterification showing high theoretical atom economy (∼94%), while the transesterification provided a low E-factor (∼0.26) and high atom efficiency (∼87.7%) in a wash-free gravity settling process with methanol recovery/reuse. Treatment of crude glycerol as a byproduct further improves the material efficiency. The results demonstrate a robust and scalable pathway for WCO biodiesel that combines statistical optimization with sustainability assessment, delivering high conversion with reduced material intensity and waste, and offering an adaptable framework for other high FFA feedstocks.

Introduction

The growing concern over climate change and the environmental impacts of fossil fuels has intensified the global search for sustainable energy alternatives. Biodiesel has emerged as a viable alternative to petroleum diesel because it is biodegradable, renewable, and produces lower emissions of regulated pollutants. , Conventionally, biodiesel is synthesized from edible vegetable oils (palm, soybean, sunflower) and from nonedible sources (jatropha, castor, animal fats). However, dependence on edible oils drives feedstock costs up to ∼70% of total production, raising concerns about the trade-off between food and fuel. − In contrast, WCO is a cost-effective and abundant feedstock, with ∼27 million tons generated globally in 2015, of which around 60% were improperly disposed of, contributing to water pollution and public health risks. , Valorizing WCO into biodiesel addresses these disposal issues and aligns with circular economy principles by converting waste into clean energy.

Despite its advantages, WCO presents processing challenges due to its typically high free fatty acid (FFA) content (>5 wt %). Under direct alkaline transesterification, FFAs form soaps that cause emulsions, low yields, and difficult phase separation. , A common solution is acid-catalyzed esterification pretreatment to reduce FFA to <1 wt % before base transesterification, with performance governed by methanol-to-oil ratio, catalyst loading, and reaction time. ,, At the same time, recent advances show heterogeneous and bifunctional catalysts capable of one-pot esterification–transesterification of high-FFA feedstocks (e.g., sulfonated carbons/silicas, supported heteropolyacids, Fe₃O₄–SO₃H and other acid-functionalized nanoparticles, ion-exchange resins, and tailored acid–base bifunctionals), often enhanced by sonication to accelerate mass transfer. ,− These routes offer operational advantages (catalyst recovery/reuse, lower methanol excess, and shorter times). However, most reports remain laboratory-scale; scale-up is limited by deactivation and/or leaching, sensitivity to feedstock heterogeneity (water, food residues, mixed oil origins), and catalyst fabrication/regeneration costs. Consequently, while one-pot systems are a promising direction, the two-step sequence (acid esterification and base transesterification) remains widely used in pilot/industrial contexts for its robustness and scalability. ,

Decades of work have optimized biodiesel synthesis by tuning the reaction variables and reactor configurations. For high-FFA WCO, two broad routes dominate: (i) a two-step sequence, acid esterification to lower acid value followed by base transesterification, and (ii) one-pot pathways using heterogeneous or bifunctional catalysts capable of driving esterification and transesterification simultaneously. , Most optimization studies use design of experiments and RSM to map the effects and interactions of alcohol-to-oil ratio, catalyst loading, temperature, and time on a single response (typically FFA reduction or FAME yield). , This approach is powerful for locating statistically robust operating windows and for quantifying trade-offs among kinetic drivers (alcohol excess, acidity, and residence time). However, single-response optimization can inadvertently favor conditions that are chemically efficient but operationally burdensome, for example, due to high solvent inventories, difficult workup, or long residence times.

Green chemistry offers a design framework for reducing hazards and waste throughout the process lifecycle, synthesized in principles that prioritize prevention, atom economy, the use of safer solvents and auxiliaries, energy efficiency, and catalysis, among others. , To put these principles into practice, green metrics are used to quantify performance beyond yield: Atom Economy and Atom Efficiency evaluate stoichiometric utilization; E-factor and Process Mass Intensity (PMI) measure waste and input generation per unit of product; and Reaction Mass Efficiency (RME) integrates conversion and selectivity in terms of mass. ,− In the case of biodiesel, there are few studies related to the use of green metrics; these metrics are especially relevant due to the impact of methanol inventories, acid/base consumption, byproduct handling (e.g., glycerol), and operating energy requirements.

This study adopts a two-stage strategy. First, response surface methodology (Box–Behnken at 60 °C) is used to model and optimize the esterification step as a single DOE response (FAME conversion), quantifying the effects and interactions of the methanol-to-oleic-acid ratio, acid-catalyst loading, and reaction time. Second, the downstream transesterification is evaluated experimentally, and green chemistry metricsAtom Economy, Atom Efficiency, E-factor, Process Mass Intensity, Reaction Mass Efficiency, and Mass Productivityare computed for every experimental condition and for the full two-stage route under a no-wash workup with methanol recovery. Reporting these metrics side by side enables the transparent identification of operating windows that combine high conversion with lower material intensity and reduced residues, providing a robust, scalable framework for WCO biodiesel consistent with green chemistry principles.

Materials and Methods

Raw Materials and Characterization

The WCO used in this study was obtained from a collection center at the Supply Center in Mexico City, Mexico. Before the esterification and transesterification reactions, WCO was filtered to remove solid impurities. The oil was then characterized for its physical and chemical properties, which is crucial for optimizing experimental conditions.

High-purity reagents were used, including 98% sulfuric acid (H₂SO₄), 99.9% methanol (CH₃OH), 99.5% oleic acid, and sodium hydroxide (NaOH). All chemicals were used as received to maintain consistency and reproducibility in the experimental results. The experiments were conducted in triplicate to ensure statistically significant and reliable data.

FFA contents in the WCO were determined using the titration method according to AOCS Ca 5a-40 (1997), and the acidity index was calculated as the milligrams of NaOH required to neutralize the FFA per gram of oil (eq ).

The acidity index can be represented as

$$\mathrm{Acidity\; index}=\frac{V\times N\times M_{\mathrm{NaOH}}}{m_{\mathrm{sample}}}$$ 1

With the acidity index (g NaOH/g oil), V _NaOH volume (ml), N _NaOH the normality (0.1N), M _NaOH molar mass (g/mol), oil mass (g), and 28.2 FFA such as oleic acid. Thus, the FFA (%) was calculated utilizing eq :

$$\mathrm{FFA}(\%)=\frac{V\times N\times 28.2}{m_{\mathrm{sample}}}$$ 2

Optimization of the Oleic Acid Esterification Process

Oleic acid esterification was carried out to identify operating conditions that maximize the material efficiency and FAME yield. The literature agrees that the critical variables are the methanol:oleic acid molar ratio, catalyst concentration, and reaction time. − Furthermore, several studies have shown that 60 °C is a suitable temperature for acid esterification, balancing kinetic speed and methanol losses; therefore, in this work, it was kept constant at 60 °C. , Consequently, the methanol:oleic acid ratio, H₂SO₄ loading, and reaction time were defined as control variables; their levels and experimental design are detailed in Table . ,,

1. Range of Parameters for Esterification Using the Box–Behnken Method.

Independent variable	Unit	Minimum (−1)	Central (0)	Maximum (+1)
Methanol:oleic acid ratio	-	2:1	5.5	9:1
Catalyst	%	2	6	10
Time	min	30	315	600

The temperature was maintained at 60 °C to prevent methanol volatilization, ensuring that it remained in the liquid phase and was effectively involved in the reaction. Agitation was set at 400 rpm to ensure homogeneous mixing. For the experiments, 30 g of oleic acid was placed in a two-neck round-bottom flask. The flask was heated on a stirring hot plate and equipped with a controlled cooling system to minimize the reactant losses.

Oleic acid was chosen as the free fatty acid model due to its high prevalence in WCO and its low-cost commercial availability, making it suitable for simulating WCO under experimental conditions. ,, A Box–Behnken experimental design within response surface methodology (RSM) was used to optimize the process. , Model fitting to a second-order polynomial, ANOVA, and numerical optimization (to maximize predicted FAME conversion) were performed in STATISTICA v8 (StatSoft, Inc., Tulsa, OK, USA). This approach efficiently evaluates interactions among key variables with fewer experiments, optimizing resources and study time (Table ).

An experimental matrix was established using the Box–Behnken experimental design and the operational parameters selected in Table , reducing the number of experiments to 15 runs (Table ). This approach optimizes the esterification process of oleic acid by identifying the optimal operating conditions through mathematical calculations within the experimental domain. This methodology minimizes the number of required experiments, saving resources and time, while ensuring an efficient evaluation of the key variables in the process.

2. Experimental Design Matrix.

Run	Methanol:oleic acid ratio	Catalyst (%)	Time (min)	FAME Yield (%)
1	2	6	30	53.01
2	5.5	2	30	83.98
3	5.5	10	30	87.39
4	9	6	30	91.99
5	2	10	315	94.56
6	2	2	315	78.14
7	5.5	6	315	98.31
8	5.5	6	315	98.55
9	5.5	6	315	98.43
10	9	2	315	98.61
11	9	10	315	98.31
12	2	6	600	91.96
13	5.5	2	600	97.28
14	5.5	10	600	98.41
15	9	6	600	98.48

^aCenter-point runs (runs 7–9) were performed in triplicate and are reported as 98.43 ± 0.12% standard deviation (n = 3).

A new experimental run (Table ) was conducted with the selected variables to verify the optimized values, taking samples at regular intervals. A monitoring curve was generated to track the progress of the reaction over time.

Esterification and Transesterification of WCO

Esterification was conducted to reduce the FFA content in WCO under the optimized conditions from the experimental design. A total of 30 g of WCO was added to a 250 mL two-neck round-bottom flask with a magnetic stirrer and cooling system to maintain 60 °C. With a stirring speed of 400 rpm, the stoichiometry of the reaction, based on oleic acid (282 g/mol) and methanol (32 g/mol), was calculated to match the WCO FFA content (8.12%), ensuring maximum conversion of oleic acid to esters while minimizing byproducts. The reaction mixture was stirred for 60 min and left to rest for 12 h for phase separation, yielding esterified WCO, water, and methanol. The acid number was analyzed to confirm FFA reduction, and residual methanol was evaporated and reused, enhancing the process efficiency.

Subsequent transesterification used a 6:1 methanol-to-oil molar ratio and 1% sodium hydroxide (NaOH) as the catalyst. The reaction, conducted at 60 °C and 400 rpm for 60 min, produced methyl esters (biodiesel). Samples were taken at intervals to monitor the conversion progress.

After the reaction, the mixture was allowed to stand quiescently for 24 h at ambient temperature, leading to gravitational phase separation into an upper FAME-rich layer and a lower crude-glycerol layer containing the polar/ionic species (residual homogeneous catalyst, soaps/salts) and dissolved methanol. The FAME layer was decanted, and the excess methanol was recovered by vacuum distillation (no aqueous washing) and returned to the solvent inventory for subsequent batches. The CG phase was collected separately for downstream handling/valorization. When required for analysis, the FAME phase was polished without water (gravity filtration through a neutral dry medium) and dried under reduced pressure to remove residual methanol before characterization. No water was used at any point in the workup, and therefore, wash water does not enter the material balances underlying PMI and E-factor.

Fourier Transform Infrared Spectroscopy (FTIR) Analysis

FTIR analysis was utilized to characterize the products and confirm the effective conversion of triglycerides into FAME, ensuring the quality of the produced biodiesel. A PerkinElmer Frontier spectrophotometer was used to perform both qualitative and quantitative assessments of the WCO and FAME during the esterification process. FTIR provided insights into the reaction’s progress by identifying key signals corresponding to methanol, oleic acid, and the formation of methyl esters, allowing a detailed qualitative analysis of the reaction.

Spectral data were collected through 32 scans with a resolution of 4 cm^–1, covering a range from 4000 to 600 cm^–1. For precise quantitative evaluation, the Spectrum Quant software was employed to determine the FAME concentration in biodiesel, using a calibration curve based on FAME derived from soybean oil as a reference standard. , This approach allowed for a robust analysis of the biodiesel quality, ensuring consistency and reliability in the characterization of the esterification products.

Biodiesel Properties

Fuel properties were determined as follows: kinematic viscosity at 40 °C (ASTM D445), density at 15 °C (ASTM D4052), acid value (ASTM D664), ester content (EN 14103, GC-FID), cloud point (ASTM D2500), and pour point (ASTM D97). The FAME profile was obtained by GC-FID (EN 14103). The cetane number for neat biodiesel was estimated from the FAME composition using published correlations (Knothe, 2014); direct CN measurement (ASTM D613 or ASTM D6890) was not available with our instrumentation configured for petrodiesel/B-blend cetane index.

Analysis of FAME by Gas Chromatography

The identification and quantification of FAME were conducted using a Clarus 580 gas chromatograph (PerkinElmer EU) equipped with a flame ionization detector (FID) and an Elite-5 column (5% diphenyl-95% dimethyl polysiloxane), measuring 30 m in length, with an internal diameter of 0.25 mm and a film thickness of 0.25 μm. The operating conditions were set with an oven temperature program starting at 100 °C (held for 3 min) and increasing at 20 °C/min to 280 °C (held for 8 min). Both the injector and detector temperatures were maintained at 260 °C using a split/splitless injector mode with a 1:5 split ratio, and nitrogen was used as the carrier gas at 30 psi. The analyses were conducted in duplicate.

Before chromatographic analysis, samples were diluted with 98.5% HPLC-grade hexane. The quantification of FAME was achieved through interpolation using calibration curves prepared for each analyte.

Green Chemistry Metrics in Esterification and Transesterification of WCO

The application of green chemistry metrics (GCM) is crucial in the study of esterification and transesterification processes, as it provides a quantitative framework for assessing the environmental, economic, and safety impacts associated with biodiesel production. By integrating GCM, the study’s focus expands beyond improving biodiesel yield to include waste minimization, energy reduction, and the identification of safer and more sustainable alternatives for catalysts and reactants.

As shown in Table , the data presented were used as the basis for determining the green chemistry parameters and evaluating the process efficiency and the minimization of byproducts, which is crucial for optimizing biodiesel yield and ensuring a more sustainable process.

3. Material Balance of Inputs, Reactants, and Products in the Esterification and Transesterification of Waste Vegetable Oil .

Type	Compounds	Esterification mass (g)	Transesterification mass (g)
Reactants	WCO	2.43	27.57
Inputs	Methanol	2.32	3.6
	Sulfuric acid	0.05	0
	Sodium hydroxide	0	0.28
Reactants and inputs total		4.8	31.45
Products	Methyl ester	1.7	24.19
Byproducts	Crude glycerol	0	3.92
Total products		1.7	28.11
Residues	Soaps	0.88	0
	Sodium sulfate	0.07	0
	Water	0.17	0
	Methanol	1.2	0
Total residues		3.1	3.92

^aNo-wash workup (gravity decantation + MeOH (methanol) recovery/reuse). E-factor computed as mass of residues/mass of FAME on a fresh-materials basis (also for PMI). Residues include only reaction water, soaps, and unrecovered MeOH in esterification; recovered MeOH is not counted in transesterification.

To evaluate the sustainability of the esterification and transesterification processes, several green chemistry metrics were applied:

The green chemistry metrics reported in this work were calculated from the reaction stoichiometry. All stoichiometric calculations follow the general reaction notation shown in eq :

$$a(\mathrm{A})+b(\mathrm{B})\to c(\mathrm{C})+d(\mathrm{D})$$ 3

where A is the limiting reagent, B the coreagent, C the principal product, and D a byproduct; a, b, c, and d are the corresponding stoichiometric coefficients. For the present process, the two-step reactions were explicitly considered to be used experimentally:

Esterification:

$$\mathrm{Oleic\; acid}(\mathrm{A})+\mathrm{MeOH}(\mathrm{B})\to \mathrm{Methyloleate}(\mathrm{C})+\mathrm{water}(\mathrm{D})$$ 4

Transesterification:

$$\mathrm{Triolein}(\mathrm{A})+\mathrm{3MeOH}(\mathrm{B})\to \mathrm{3FAME}(\mathrm{C})+\mathrm{crude\; glycerol}(\mathrm{D})$$ 5

Stoichiometric coefficients (a–d) and molecular weights used in atomic economy/atom-efficiency calculations are listed in the Methods and in the Supporting Information (we used triolein as the TG model with M _W = 885.43 g·mol^–1, oleic acid M _W = 282.46 g·mol^–1, MeOH M _W = 32.04 g·mol^–1, and a weighted-average FAME M _W,avg ² ≈ 87.0 g·mol^–1 derived from GC-FID composition). This stoichiometric basis was complemented with experimental mass-balance data (inputs, products, and residues) for each run to compute the green chemistry metrics reported (atom economy, atom efficiency, yield, RME, E-factor, and PMI).

E-Factor

The E-factor, proposed by Roger Sheldon (2007), is the dimensionless ratio of the total mass of waste generated to the mass of biodiesel (FAME) produced, calculated here on a fresh-materials basis. ,, Because a water-free workup was used (cold decantation with MeOH recovery/reuse), no wash water is counted as waste. In esterification, the residues considered are reaction water, neutralization salts/soaps, and unrecovered MeOH (Table ). In transesterification, two common ways to account for waste are reported in the literature: (i) the Gude et al. (2018) approach, which counts crude glycerol (CG), unconverted oil, and unrecovered MeOH as waste; and (ii) the CG-valorization approach (used here as the base case, since CG is easily separated by decantation and viable reuse routes exist), in which CG is treated as a byproduct and only unconverted oil and unrecovered MeOH are counted as waste.

$$\mathrm{E}-\mathrm{factor}=\frac{m_{\mathrm{residuos,total}}(\mathrm{g})}{m_{\mathrm{product}}(\mathrm{g})}$$ 6

where m _waste,total is the total mass of residues (as defined above) and m _product is the mass of FAME obtained.

Atomic Economy

Atomic economy was calculated for each reaction from stoichiometry and molar masses, incorporating experimental data where appropriate (e.g., the weighted-average molecular weight of the FAME mixture derived from GC–FID analysis). The general reaction notation used was a(A) + b(B) → c(C) + d(D), where A is the limiting reagent (oleic acid or WCO, represented when required by a triglyceride model), B is methanol and catalyst, C is the desired methyl ester (FAME), and D is a byproduct (H₂O or glycerol). AE was computed as ,

$$\mathrm{Atomic\; economy}(\%)=\frac{M_{\mathrm{W}}\mathrm{of\; C}\left(\frac{\mathrm{g}}{\mathrm{mol}}\right)}{M_{\mathrm{W}}\mathrm{of\; A}\left(\frac{\mathrm{g}}{\mathrm{mol}}\right)+M_{\mathrm{W}}\mathrm{of\; B}\left(\frac{\mathrm{g}}{\mathrm{mol}}\right)}\times 100$$ 7

Atom Efficiency

Atom efficiency was calculated as the product of the atom economy and the experimentally measured yield (esterification and transesterification), thereby combining stoichiometric potential with actual conversion: ,

$$\mathrm{Atom\; efficiency}(\%)=\frac{\mathrm{Atomic\; economy}(\mathrm{\%})}{\mathrm{FAME\; yield}(\mathrm{\%})}\times 100$$ 8

FAME Yield

The experimental FAME yield (%) was determined gravimetrically as the ratio of the mass of isolated fatty acid methyl esters after transesterification and solvent recovery (m _FAME, g) to the initial mass of oil charged to the reactor (m _oil, g), multiplied by 100 (eq ). Unless stated otherwise, both masses are reported on a dry basis.

$$\mathrm{FAME\; yield}(\%)=\frac{m_{\mathrm{FAME}}(\mathrm{g})}{m_{\mathrm{oil}}(\mathrm{g})}\times 100\%$$ 9

Process Mass Intensity

Evaluates the total materials used per product unit, focusing on resource reduction and waste minimization. It considers reactants, solvents, and catalysts used, emphasizing sustainability. ,

$$\mathrm{Process\; mass\; intensity}=\frac{\mathrm{Total\; mass\; in\; the\; process}(\mathrm{g})}{\mathrm{Mass\; of\; final\; product}(\mathrm{g})}$$ 10

Mass Productivity

Calculates mass productivity, defined as the inverse of the Mass Productivity Index (MPI), commonly used to assess synthesis efficiency in industrial operations.

$$\mathrm{Mass\; Productivity}=\frac{1}{\mathrm{PMI}}\times 100\%$$ 11

Reaction Mass Efficiency

Assesses optimal and suboptimal reaction conditions, considering the E-factor, atom economy, and stoichiometry. It helps estimate the environmental impacts of processes.

$$\mathrm{Reaction\; Mass\; Efficiency}(\%)=\frac{1}{1+\mathrm{E}-\mathrm{factor}}\times 100\mathrm{\%}$$ 12

Environmental Impact Factor f of Solvents and Catalysts

Evaluate the environmental effects of solvents and catalysts, aiming to minimize toxicity. A zero value indicates full recycling and proper disposal; otherwise, it reflects unmanaged waste. ,

$$\mathrm{Environmental\; Impact\; Factor}f\mathrm{of\; Solvents\; and\; Catalysts}\left(\frac{\mathrm{g}}{\mathrm{g}}\right)=\sum \frac{\mathrm{Mass\; of\; the\; reactant,\; solvent\; and\; catalyst}}{\mathrm{Mass\; of\; the\; product}}$$ 13

Results and Discussion

Model Fitting and Statistical Analysis

The analysis of variance (ANOVA) results for the esterification process (Table ) reveal that the methanol-to-oleic acid molar ratio and reaction time were the most significant variables influencing ester yield. Both linear (L) and quadratic (Q) components of these factors had p-values below 0.05, confirming their strong effect on the model (F = 23.52 and 6.92 for ratio; F = 23.54 and 8.25 for time, respectively). These findings align with previous reports that emphasize the importance of optimizing the molar ratio and residence time in biodiesel synthesis to improve both yield and process efficiency. ,

4. Analysis of ANOVA for the Esterification in Different Conditions.

Factor	SS	DF	MS	F	p-value
(A) Methanol:oleic acid ratio (L)	607.79	1	607.79	23.52	0.0046
Methanol:oleic acid ratio (Q)	178.84	1	178.84	6.92	0.0464
(B) Catalyst concentration (%) (L)	53.33	1	53.33	2.06	0.2102
Catalyst concentration (%) (Q)	3.28	1	3.28	0.12	0.7361
(C)Time (min) (L)	608.30	1	608.30	23.54	0.0046
Time (min) (Q)	213.31	1	213.31	8.25	0.0348
AB	69.87	1	69.87	2.70	0.1610
AC	263.51	1	263.51	10.19	0.0241
BC	1.300	1	1.29	0.05	0.8314
Error	129.19	5	25.83
Total SS	2112.26	14

^aSS: Sum of Square.

^bMS: Medium square.

In contrast, the catalyst concentration (H₂SO₄) did not show a statistically significant impact within the studied range (2–10%), with p-values of 0.2102 (L) and 0.7361 (Q). This suggests that even at low acid concentrations, the esterification reaction proceeded effectively, possibly due to sufficient catalytic activity already being achieved. Consistent with prior reports, acid catalysis ceased to be the rate-limiting step once the minimum activation thresholds (temperature/acid loading) were reached. ,,

Among the interaction terms, only the interaction between reaction time and methanol:oleic acid ratio (AC) was statistically significant (F = 10.19, p = 0.0241). This implies that the efficiency of the esterification process depends on the simultaneous adjustment of both variables, reinforcing the rationale behind using the RSM to capture such nonlinear behavior. The remaining interaction terms (AB and BC) showed no significant effect (p > 0.1), suggesting that within the experimental domain, these factors behaved independently.

The model’s adequacy was confirmed through high F-values for the regression terms and a satisfactory coefficient of determination (R ²), ensuring a reliable prediction of esterification efficiency. These results also provide a solid foundation for the subsequent multiobjective optimization, where not only yield but also sustainability indicators such as E-Factor and atom economy are integrated into a comprehensive evaluation framework.

A constant temperature of 60 °C was used for all experiments in the RSM matrix (with SD ≤ ± 2 °C). The temperature used in the study falls within the commonly reported range of 50–65 °C for acid-catalyzed esterification, balancing kinetic efficiency with minimizing solvent losses. Reactions were carried out under reflux using a thermostatic bath; mixtures were allowed to equilibrate before timing, and the temperature was recorded throughout the process.

Effect of Variables on Esterification

The optimization of the esterification process was performed by evaluating three independent variables: methanol:oleic acid molar ratio (2:1–9:1), catalyst concentration (2–10%), and reaction time (30–600 min), at a constant temperature of 60 °C. The resulting second-order polynomial model included linear, quadratic, and interaction terms, exhibiting an R ² of 0.7804. This indicates that approximately 78% of the variability in the conversion to FAME is explained by the selected variables and their interactions.

Figure A shows the response surface for catalyst concentration and molar ratio: a low yield (53%) was observed at a 2:1 ratio and 6% catalyst (Run 1), likely due to methanol deficiency; in contrast, 98.23% was reached at 9:1 with 10% catalyst (Run 11), while 98.31% was maintained at 5.5:1 with 6% catalyst, indicating that high conversion is possible at lower alcohol and moderate acid levels, a relevant green chemistry consideration.

1.

Response surfaces of FAME conversion as a function of: (A) catalyst concentration and methanol:oleic acid ratio; (B) time and methanol:oleic acid ratio; (C) time and catalyst concentration.

In Figure B, the molar ratio–time interaction is evident: low yields at short times and small ratios (<60% at 30 min and 2:1) increase sharply at higher ratios and longer times (>95% at 315 min and 5.5:1–9:1). Figure C confirms diminishing returns above ∼6% catalyst; values >10% may even favor darkening and byproduct formation. ,

The molar ratio is the most sensitive factor in FAME conversion, followed by reaction time, while the catalyst concentration is particularly relevant at low levels. According to response surface methodology (RSM), the predicted statistical optimum, defined a priori as the critical point for end-of-study validation, was located at 8.44:1 methanol:oleic acid, 2% catalyst, and 363.11 min with a predicted conversion of approximately 100%. Similar behavior was observed by Mansir et al. (2018) and Al-Sakkari et al. (2020), who reported increased conversion with higher molar ratios but noted economic and environmental drawbacks beyond a certain threshold.

Esterification Step (Oleic Acid): Kinetic Validation and FTIR Monitoring

To validate the esterification optimum predicted by RSM (60 °C, methanol:oleic acid = 8.44:1, catalyst = 2 wt %), we performed a kinetic run and monitored conversion over time (Figure ).

2.

Esterification step (oleic acid → methyl oleate): kinetic profile of FAME formation at 60 °C, methanol:oleic acid = 8.44:1, H₂SO₄ = 2 wt %.

The results showed a rapid increase in conversion during the initial reaction phase, with 90% FAME yield achieved within the first 30 min and a plateau at 94% reached by 90 min (Figure ). Beyond this point, no significant increase in conversion was observed, indicating that the reaction reached equilibrium or diffusion limitations became dominant. This plateau behavior suggests that extending the reaction time beyond 90 min offers minimal benefit in terms of yield but increases energy consumption and operating time, key considerations in sustainable process design.

Therefore, the optimal practical conditions were adjusted to a reaction time of 90 min, 2% catalyst, and an 8.44:1 molar ratio, yielding 94% conversion. These results confirm the robustness of the model and align with previous studies that identified similar operating windows. For instance, Al-Sakkari et al. (2020) and Chai et al. (2014b) reported optimal molar ratios close to 9:1 and reaction times between 60 and 120 min under comparable conditions. Aworanti et al. (2019) similarly highlighted that catalyst concentrations above 2% often yield diminishing returns, while lower values compromise reaction efficiency.

The 90-min plateau at ∼94% conversion agrees with prior reports at ∼60–65 °C and a ∼9:1 methanol:oleic acid ratio. , This validation not only confirms the predictive capacity of the RSM-based model but also highlights that multiobjective optimization allows for the refinement of reaction conditions, minimizing energy and reagent use without sacrificing yield, thus reinforcing the integration of sustainability metrics such as atom economy and GEI.

Figure shows the FTIR spectra of samples collected at 10, 15, 30, 60, and 90 min during the esterification of oleic acid (60 °C; methanol:oleic acid = 8.44:1; H₂SO₄ = 2 wt %). The most prominent band corresponds to the acid carbonyl at ∼1708 cm^–1, accompanied by the broad O–H dimer envelope at ∼2500–3300 cm^–1; both decrease progressively as the reaction proceeds, evidencing consumption of FFA. In parallel, the ester carbonyl band at ∼1740–1744 cm^–1 grows and the C–O–C/O–CH₃ vibrations at ∼1196–1170 cm^–1 and ∼1436 cm^–1 intensify, confirming methyl-ester formation. The olefinic C–H (∼3005 cm^–1), CH₂ stretching (∼2923/2853 cm^–1), and long-chain rocking (∼724 cm^–1) bands remain essentially unchanged, indicating conservation of the alkyl chain.

3.

Esterification step: FTIR spectra at 10, 15, 30, 60, and 90 min showed consumption of FFA ((CO) ≈ 1708 cm^–1) and formation of methyl ester bands.

Qualitatively, a marked decrease in the 1708 cm^–1 band is observed between 0 and 60 min, which levels off between 60 and 90 min, in agreement with the kinetic profile in Figure . At 90 min, the acid carbonyl is markedly attenuated, consistent with ∼94% conversion; extending the time beyond this window provides no meaningful gain in ester formation and only increases energy consumption. These spectral evolutions agree with previous FTIR-based biodiesel studies by Abdullah et al. (2021) and Lamichhane et al., (2020) and with time-efficiency recommendations (>90% conversion in 60–90 min) reported by Wongwuttanasatian et al. (2023) and Zhang et al. (2024).

WCO Biodiesel Quality and Standard Compliance

The biodiesel properties obtained in this study meet ASTM D6751 and EN 14214 and fall within the typical ranges reported for WCO-derived fuels (Table ). The kinematic viscosity (4.63 mm² s^–1) and density (865.9 kg m^–3) match the intervals described by Kumar Mishra et al. (2021) and Ghazanfari et al. (2017) for monounsaturated-rich biodiesel, while the acid value (0.44 mg KOH g^–1), below 0.50 mg KOH g^–1, confirms effective pretreatment and is comparable to values achieved by two-step schemes (esterification/transesterification) for feeds with FFA > 4–5%. , The ester content (96.79% w/w) remains within the EN limit (≥96.5%) (Table ), demonstrating high conversion under moderate conditions (60 °C, no water washing). Thus, these results indicate that this route remains a viable and sustainable alternative compared with heterogeneous catalyst or ultrasound methods, which are efficient but still under evaluation for scale-up.

5. Properties of Biodiesel Compared to ASTM D6751 and EN 14214 Standards.

Property	Units	Biodiesel	Limits ASTM D6751	Limits EN14214
Kinetic viscosity 40 °C	mm2/s	4.6298	1.9–6.0	3.5–5
Density	kg/cm3	865.91	820–900	860–900
Acid index	mg KOH/g	0.44	Max 0.50
Ester	% mass	96.79	-	96.5
Cloud point	°C	3	–3 to 12	-
Pour point	°C	8	–15 to 10	-
Calorific value	MJ/kg	39.92	35 to 45	-
Cetane number	min	56–58	47	51
Ash content	%	<1	0.02 max
Methyl oleate (C18:1)	%	75.58	-	-
Methyl palmitate (C16:0)	%	20.20	-	-
Methyl linoleate (C18:2)	%	2.82	-	-

^aAccording to Knothe (2014).

The FAME profile is dominated by methyl oleate (C18:1, 75.6%), with C16:0 (20.2%) and C18:2 (2.8%). This distribution is typical of WCO and provides a balance between low-temperature behavior and oxidative stability. Monounsaturated fractions improve stability relative to highly polyunsaturated fractions while avoiding the cold-flow penalties of highly saturated fractions, consistent with Kumar Mishra et al. (2021) and Elgharbawy et al. (2021). In more saturated systems (for example, palm oil), Ghazanfari et al. (2017) also reported on-spec viscosity and density but with penalties in cold-flow properties and the need for additional NOx optimization; our high C18:1 content suggests a more favorable trade-off.

The cetane number was not measured directly; based on the composition–property correlations reported by Knothe (2014), it was estimated at ∼56–58 from the fatty acid profile, exceeding the ASTM (≥47) and EN (≥51) minima and consistent with the high C18:1 content observed in this study. The cloud point (3 °C) and pour point (8 °C) are in the expected range for monounsaturated fatty acid-rich biodiesel; although EN regulates CFPP (Cold Filter Plugging Point) by climate class, these values indicate that blending or cold-flow improvers may be required for severe winter grades.

In this study, the results agree with studies demonstrating the competitiveness of the two-step route for high-FFA feedstocks, meeting specifications with low methanol use and mild conditions and positioning WCO, even when moderately degraded, as a reliable and sustainable resource for high-quality biodiesel when processed under a material-efficient, optimized design.

Figure C (raw WCO) shows a strong band at ∼1708 cm^–1 assigned to the acid carbonyl (CO) of FFAs, together with CH at ∼3010 cm^–1 (cis double bonds), intense aliphatic C–H stretches at 2923/2853 cm^–1, and weak ester C–O features of residual triglycerides in the 1240–1160 cm^–1 region.

4.

FTIR spectra of (A) crude WCO, (B) esterified WCO, and (C) FAME, evidencing FFA-to-FAME transformation by loss of the ∼1708 cm^–1 acid CO and growth of the 1740–1749 cm^–1 ester CO.

After esterification (Figure B), the ∼1708 cm^–1 acid band is markedly attenuated, while the ester carbonyl in 1740–1749 cm^–1 grows, accompanied by increased intensity in the 1240–1160 cm^–1 region (C–O–C stretching) and a shoulder near ∼1196 cm^–1 (O–CH₃). , These changes indicate partial conversion of FFAs to methyl esters and an effective pretreatment of the subsequent base step.

The final biodiesel (Figure A) is dominated by the ester CO in 1740–1749 cm^–1; the ∼1708 cm^–1 acid band is absent within the detection limits, indicating negligible FFAs. Strong aliphatic C–H stretches at 2923/2853 cm^–1, bending modes around 1465–1435 cm^–1, and the −(CH₂)_n rocking at ∼724 cm^–1 confirm the long-chain alkyl nature of the FAMEs. The C–O envelope (1240–1160 cm^–1) with a feature near ∼1196 cm^–1 is also characteristic of methyl esters. ,

The raw WCO spectrum (C) (Figure ) shows a strong absorption at 1708 cm^–1, corresponding to the CO stretching of free fatty acids (carboxylic acid groups), and peaks at 3010 cm^–1 (CH stretching of cis-double bonds) and 2923/2855 cm^–1 for C–H stretching in aliphatic chains. Additionally, bands at 1378 cm^–1 and 1165 cm^–1 confirm the presence of ester bonds already in the oil due to residual triglycerides.

Therefore, Figure shows the spectral evolution from crude WCO, through the esterified intermediate, to the final biodiesel; the attenuation of the acid carbonyl (∼1708 cm^–1) and the growth of the ester carbonyl (1740–1749 cm^–1) confirm the conversion of WCO and the formation of fatty acid methyl esters (FAME). These findings are consistent with the measured physicochemical properties and the FAME profile obtained in this study (Table ).

Green Chemistry Metrics for Esterification and Transesterification

The incorporation of green chemistry metrics into biodiesel production is critical because it translates high conversion into efficient atom utilization and low residue generation, factors that determine cost, operability, and environmental impact. ,, These metrics quantify resource use and waste, guiding the choice of conditions that use fewer reagents, shorten reaction times, and simplify separations, which are crucial for sustainable scale-up. Combining RSM with green chemistry metrics (GCM) enables mapping of the operating space and selecting practical windows that deliver high FAME conversion with minimal residues for WCO-based biodiesel. ,

To assess sustainability beyond conversion, Atom Economy (AE), E-factor, and Mass Productivity (MP) were evaluated alongside FFA/FAME conversion (Table ). Among the conditions examined, the 9:1, 2% catalyst, 30 min case (Condition D) consistently shows the most favorable profile: AE = 88.7%, E-factor = 0.28, MP = 84.3%, and FAME conversion = 96.5%. The combination of a sufficiently high methanol:oleic acid ratio with short residence time and low acid loading limits residue formation (lower E-factor) and improves material use (higher MP).

6. Green Chemistry Metrics and FFA/FAME Conversion for Selected Esterification Scenarios.

Condition	Methanol:oleic acid ratio	Catalyst (%)	Time (min)	Atomic economy (%)	E-Factor	MP (%)	FFA Conv. (%)	FAME Conv. (%)
A	3:1	6	600	85.3	0.41	79.1	91.2	93.4
B	5.5:1	6	315	87.1	0.35	82.4	94.5	95.1
C	7:1	4	180	83.8	0.50	76.9	88.3	91.2
Optimal	9:1	2	30	88.7	0.28	84.3	94.2	96.5

Condition B (5.5:1, 6%, 315 min) achieves high conversion (95.1%) but with a higher E-factor (0.35) and slightly lower MP (82.4%), reflecting greater material intensity due to longer time and higher catalyst. “Scenario A” (3:1, 6%, 600 min) underperforms in both conversion (93.4%) and E-factor (0.41), consistent with methanol deficiency. “Scenario C” (7:1, 4%, 180 min) is the least favorable overall (E-factor = 0.50; MP = 76.9%), illustrating that reducing both methanol and catalyst while extending time increases waste without compensating gains in conversion.

Taken together, these results confirm that the methanol-to-FFA ratio is the dominant factor influencing esterification performance, while time and acid loading exhibit diminishing returns beyond a moderate level. The metrics support a high-performance window at ratios of ≥9:1, with minimal catalyst and short times, aligning with green chemistry goals of reduced residues and improved resource efficiency. ,

To visually compare the sustainability performance of selected experimental conditions, a radar chart was constructed using four key metrics: FFA conversion, FAME conversion, Atom Economy, and E-Factor. The chart (Figure ) demonstrates that Condition B outperformed Conditions A and C across all evaluated metrics, showing a more balanced and efficient profile in terms of both chemical conversion and environmental impact.

5.

Radar chart comparing green chemistry metrics under different experimental conditions for FAME production.

Condition B, which involved a methanol-to-oil ratio of 5.5:1, 6% catalyst, and 315 min of reaction, achieved the highest normalized values in FFA and FAME conversion while maintaining a relatively low E-Factor and high atom economy (Figure ). These results suggest that even without the shortest time or lowest catalyst load, an optimal balance among variables can significantly enhance the sustainability profile of the biodiesel production process.

In contrast, Condition C (Figure ) displayed the weakest performance, particularly in conversion metrics and atom economy, indicating increased reagent waste and reduced process efficiency. Condition A, although better than Condition C, showed limited conversion and moderate atom economy, leading to a more constrained sustainability profile.

The radar chart supports the results from Table and emphasizes the value of integrating green chemistry metrics into optimization frameworks. Similar conclusions were reported by Islam et al. (2022), who emphasized that conventional optimization strategies based solely on yield or conversion may overlook critical sustainability parameters such as reagent efficiency and waste generation. The use of visual tools like radar plots enhances process assessment by making trade-offs between variables more explicit and facilitating multicriteria decision-making.

Table provides a stepwise view of the green chemistry metrics. Although esterification shows a high atom economy (94.28%), it also exhibits a higher E-factor (1.82) and a lower atom efficiency (69.96%), revealing greater material losses and waste formation at the pretreatment stage. This outcome is consistent with the formation of reaction water and with the contribution of neutralization residues and unrecovered MeOH at this scale, which depresses atom efficiency relative to atom economy and raises the E-factor.

7. Comparative Green Chemistry Metrics for the Esterification and Transesterification Stages Using WCO.

Parameters	Unit	Esterification	Transesterification
E-Factor	g/g	1.82	0.16
Atom economy (%)	%	94.28	89
Atom efficiency (%)	%	69.96	87.74
Mass intensity	g/g	2.82	1.12
Mass productivity	%	35	89
Reaction mass efficiency	%	35	79
Environmental Impact Factor f of Solvents and Catalysts		2.82	1.45

In contrast, transesterification displays a lower E-factor (0.26) and a higher atom efficiency (87.74%), yielding a more favorable sustainability signature. Incorporation of recovered MeOH from esterification into this step reduces fresh solvent demand and is reflected in the improved mass productivity (MP = 89%) and reaction mass efficiency (RME = 79%) reported in Table . These advantages translate into a higher Global Efficiency Index (GEI) for operating windows dominated by transesterification parameters, underscoring the value of stepwise analysis to guide selection beyond conversion alone.

These trends agree with the literature, which highlights trade-offs between chemical and environmental metrics in biodiesel synthesis. Martinez-Guerra (2017) and Gude et al. (2018) report comparable atom efficiency values and emphasize that even in intensified systems (microwave or ultrasound), atom efficiencies typically remain in the 86–88% range, closely matching our optimized conventional transesterification. This supports the competitiveness of a well-tuned two-step process with effective reagent recycling.

The treatment of crude glycerol (CG) within the E-factor is dependent on the accounting convention adopted. In Table , a conservative convention counted CG as a residue (E-factor transesterification = 0.26). However, CG is a separable stream that can be recovered and valorized: for example, Mena-Cervantes et al. (2018) report recovery/purification of CG to technical grade, while Aguilar-Aguilar et al. (2021) use CG as a feedstock for value-added products. When CG is treated as a byproduct rather than waste, the residue inventory decreases, and the E-factor improves (see SI sensitivity; in our case, the global E-factor drops from ∼0.27 to ∼0.12). This highlights that CG valorization and process integration are key levers for sustainability beyond conversion alone.

Conclusions

This study establishes a robust two-stage route for biodiesel from WCO by coupling an RSM-optimized acid esterification with base transesterification and a water-free workup. At 60 °C, the Box–Behnken model (three factors) predicted an optimum at methanol:oleic acid = 8.44:1, H₂SO₄ = 2 wt %, 363 min. Kinetic validation showed that conversion reaches ∼94% by 90 min and then plateaus, indicating 90 min as a practical endpoint that cuts energy/time with minimal loss in FFA conversion. The subsequent transesterification delivered ∼98% FAME, and the final fuel met ASTM D6751 and EN 14214 specifications with a FAME profile rich in methyl oleate (∼75.6%).

Green chemistry assessment clarified the trade-offs behind these outcomes. For esterification, the theoretical atom economy is ≈ 94.3%, contrasting with a higher E-factor (∼1.82) due to reaction water and neutralization residues; transesterification shows a lower E-factor (∼0.26) and higher mass productivity (∼84%). On a process basis, no aqueous washing (gravity decantation + MeOH recovery/reuse) prevents adding water to the inventory; crude glycerol is treated as a byproduct in the base case, with a sensitivity scenario provided when counted as residue. The methanol:FFA ratio emerges as the dominant lever, while time and acid loading display diminishing returns beyond moderate levels.

Next steps include a formal multiobjective DOE (desirability/Pareto) integrating green metrics as responses, techno-economic analysis, life-cycle assessment, and pilot-scale validation with intensified MeOH recovery and glycerol valorization. This roadmap aims to translate the present resource-efficient strategy into scalable practice within the circular bioeconomy.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c06167?goto=supporting-info.

• List of stoichiometric coefficients and molecular weights used in atomic economy or atom-efficiency calculations.(XLSX)

This research was supported from SECIHTI-Project CBF-2026-3723, SECIHTI-Project LN-2025-I4, SIP-IPN multidisciplinary Project 2377 modules SIP-20260253 and SIP-20260265 to carry out this research. We are grateful to the Laboratorio Nacional de Desarrollo y Aseguramiento de la Calidad de Biocombustibles (LaNDACBio) for allowing access to the laboratory facilities and for technical assistance.

The authors received no external funding for this work.

The authors declare no competing financial interest.