Development of Second-Generation Feedstock Towards Environmental Sustainability: Biobased Oil Extraction, Thermodynamics and Advanced Nonlinear Kinetic Modeling

2.1.

Pretreatment of feedstock

The process of seed cleaning was carried out by removing the shell or seed coat, the husk and sorting of chaff. Sufficient examination was conducted in the removal of any rotten or damaged seeds. This was crucial to ensure that when the oil was removed, there was no detritus left. The seed-nuts were broken, washed, dried, and then stored at atmospheric temperature before the oil-bearing seed-kernels were removed. Seeds were carefully heated over a small fire and sun dried to eliminate residual moisture [28, 29]. The seeds were then dried once more in an oven set at 65 °C for reduction of moisture content to 1.3% and were then ground using an electric grinder. The ground seeds were divided into several modicum standard sizes of particles (0.1 mm–0.5 mm) with model sieve plates. The imperative oil extraction process was then done with investigative grade solvents.

2.2.

Biobased oil extraction procedure

Soxhlet equipment was utilized to carry out the extraction of biobased oil using using n-hexane as the solvent. The Soxhlet extractor was connected to a condenser which received a predefined solvent (100 mL) for biobased oil extraction and pulverized neem oilseeds (10 g) of average particle size. At the range of modicum sizes of particles (0.1 to 0.5 mm) and temperatures (32–74 °C), the cycle of biobased oil extraction was carried out for 30 to 180 minutes. The extraction solvent was recovered or evaporated at 65 °C using a simple evaporation method. The % biobased oil output of the neem seeds is calculated by dividing the extracted biobased oil weight by the oilseeds weight and is shown in Equation (1).

2.3.

One-factor-at-a-time (OFAT) study

The OFAT experiments in batch-form were designed and carried out for biobased oil extraction from neem oilseeds using n-hexane solvent to study the impacts of the duration on biobased oil extraction (30–180 min), temperature (32–74 °C), and particle-size (0.1–0.5 mm) on the percentage oil output.

2.4.

Kinetic models

The kinetics of n-hexane-based biobased seed oil extraction process were investigated using six different kinetic models: Elovich’s, pseudo-second-order, hyperbolic, power law, parabolic diffusion, and pseudo-first-order models and the model equations for the kinetics are shown in Table 1.

2.5.

Statistical technique

The kinetic models’ statistical degree-of-fitness on the experimental data was assessed using the following metrics: coefficient of determination (R²), root mean squared error (RMSE), adjusted coefficient of determination (adj-R²), hybrid fractional error function (HYBRID%), absolute average relative error (AARE), Marquardt’s percent standard deviation (MPSD%), the sum of squares of the errors (SSE), standard error of estimation (SEE), and standard deviation (SD), total sum of squares (SST). The adj-R², R², AARE, RMSE, SSE, HYBRID%, SD, MPSD%, SEE, and SST were estimated using the Equations (2) through (11) [20, 24, 28, 30, 31].

N is the total sample size, y_i denotes the values of the experimental responses, denotes the values of the predicted responses, and y_i is the representation of the mean values of predicted response. The sample runs number, or data points number, is n, Pr is the predictors number, and q_exp = experimental response while q_model = model predicted response. The SSE, RMSE, HYBRID%, AARE, MPSD%, SEE, SD and SST of lower values as well as higher R² and adjusted-R² indicate a fit which is suited for convenient and practical future prediction [22, 28].

2.6.

Thermodynamics of neem oil extraction

Equations (12) to (15) were used to determine the extraction thermodynamics parameters, such as entropy, Gibb free energy, and enthalpy, in order to assess the nature as well as the viability of the oil extraction process.

In this instance, the variables are the universal gas constant (8.314 KJ/Kmol), change in entropy (𝛥S = KJ∕mol), temperature (K), and Gibbs free energy (𝛥G = KJ∕mol) [24, 28].

The oil yield (%) at temperature T is represented by Y_Te, while the proportion of oil that is left unextracted is represented by Y_ue. By plotting lnK against 1∕T, 𝛥S and 𝛥H may be computed; −𝛥H∕R is the slope, and 𝛥S∕R is the intercept. 𝛥G^∗ was computed using Equation (15).

3.1.

Temperature and time influence on neem seed oil extraction

Investigations were conducted at five distinct extraction temperature levels of 74 °C, 68, 55, 50, and, 32, time intervals of 180, 150, 105, 60 and 30 minutes, and particle-size of 0.1 mm to assess how temperature and time variations affect the yield of oil extraction. Figure 1 depicts the effect of temperature variation on the rate of biobased oil extraction from neem oilseeds with n-hexane as the extraction solvent mode.

The proportion of recovered neem oil rose with increasing time and temperature, as illustrated in Figure 1. The biobased oil yield upsurged with temperature up to 68 °C, after which additional increase in temperature resulted in meagre increase in the quantity of neem oil recovered. The practical increase in production of oil by increasing temperature is attributed to higher oil-extraction mass transfer coefficient, lower viscosity of biobased oil, improved yield of neem oil extraction and greater diffusion [32]. Furthermore, slight temperature increases result in a low fall in liquid-density, which decreases the solubility of the soluble component [23, 28, 33].

In this study, the process of biobased oil extraction from milled neem seeds was observed to be initially quick but then slowed down after 100–180 (minutes). This finding is coherent with the findings of John et al. [22, 24, 28] based on extraction of biobased oil from jatropha as well as neem seeds employing different solvents. The earliest quick process of extracting oil observed in this study was believed to be due to the oil existing on the periphery of the milled neem oilseeds, which readily dissolves in the dissolution fluid. However, as the process of biobased oil-extraction continued, this free oil became less available and the extraction process slowed down accordingly [19, 32, 34]. In broad terms, the preliminary quick eroding action and gradual diffusion-regulated regimes could explain the initial speedy rate and subsequent slow rate of extraction yields [23, 25, 34].

The yield of neem seed oil extraction with n-hexane, on another hand, grew with increasing temperature and time. At a temperature of 74 °C and a period of 150 minutes, the maximum percentage of biobased oil extraction was 42.9%.

3.2.

Implication of particle size variation on biobased-oil extraction

In general, properties of a feedstock, such as size of material particle, impact the process of extraction [22, 28, 32, 35]. The size of material particles relates to the surface area of the reaction and is a critical component in the study of oil extraction. As a result, the effects of varying particle size on oil yield were explored by doing tests with varied non-edible oil-seed particle sizes of 0.5, 0.15, 0.45, 0.3, 0.15 and 0.1 mm, and varied durations and intervals of 180, 150, 105, 60 and 30 minutes at 68 °C.

Figure 2 depicts the findings of the effect of particle size modification on the degree of oil extraction from neem oilseeds using n-hexane as the solvent agent. The graph illustrates that as the particle size of the neem oilseeds increased, the percentage of extracted biobased oil declined and smaller particle sizes resulted in increased oil yield. The lower and higher yields of biobased oil at larger and smaller particle sizes, respectively, are due to the smaller particle sizes having a surface area that is larger than the larger particles. The highest biobased oil extracted was 42.9%. This was attained with 0.1 mm particle size at 180 minutes.

In general, an improvement in yield of oil with size of particle is associated with a larger solid particles interfacial area, which gives rise to less intra-particle resistance by diffusion for particle of smaller sizes due to a diffusion of shorter path. Due to high intra-particle diffusion velocity in larger particles, the loss in oil production is considerable. As a result of the short surface area of contact and minimal diffusion of biobased oil from larger particles’ pores to the bulk of the solvent, all oil content in the larger particles was not removed. Increased milling also enhances the surface area due to smaller particle sizes, boosting the rate at which oil is extracted. This is attained by liberation of more oil and easily extracted by solvent. This phenomenon was noticeably demonstrated in this study, as the rate of biobased oil extraction from nonedible neem oilseeds was faster at smaller particles sizes than at bigger particles, owing to a shorter path of diffusion, a faster degree of mass transfer, and a faster degree of oil solubility in solvent [22, 23, 28, 35].

3.3.

Interactive effects of temperature, particle size, and extraction time on neem oil yield

To evaluate the combined effects of temperature, particle size, and extraction time on the yield of neem oil, a three-way ANOVA was conducted. This statistical method determines if the interaction between these factors significantly influences the extraction efficiency. The dependent variable in this study is neem oil yield, while the independent variables are temperature, particle size, and extraction time. By examining the interaction between these factors, it is possible to gain a better understanding of how changes in one variable affect the other variables and their collective impact on oil yield. The results of ANOVA are summarized in Table 2.

ANOVA results show that all individual factors—temperature, particle size, and extraction time—have a significant effect on neem oil yield (p < 0.0001). Additionally, the two-way interactions between temperature and particle size (F = 7.70, p < 0.0001), temperature and extraction time (F = 9.23, p < 0.0001), as well as particle size and extraction time (F = 6.07, p < 0.0001) are also statistically significant, indicating that the combined effects of these factors influence oil yield significantly.

However, the three-way interaction between temperature, particle size, and extraction time (F = 1.19, p = 0.0937) is not statistically significant. This suggests that while the individual and paired interactions among these factors have a significant impact on the oil yield, their combined interaction does not strongly affect the outcome.

The findings from this analysis align with the existing literature on oil extraction processes. Studies have consistently shown that temperature and extraction time are critical factors influencing oil yield. Prasad et al. [11] demonstrated that higher extraction temperatures promote higher oil yield due to increased solvent diffusivity, but excessive temperatures may degrade oil quality. Similarly, the effect of particle size on extraction efficiency has been documented, with smaller particle sizes improving oil release due to the greater surface area [10]. However, the interaction of these variables has received limited attention, and few studies have examined their combined effect on extraction yield. This study provides new insights into the interactive effects of these factors, emphasizing the need for optimized extraction parameters for second-generation feedstock processes [12].

ANOVA results underscore the importance of optimizing multiple parameters simultaneously to maximize yield in industrial oil extraction processes. Future work should focus on further exploring the thermodynamic and kinetic interactions between these variables using other extraction solvents, particularly in the context of nonlinear models for sustainable extraction.

3.4.

Kinetic parameters

Table 3 provides a comprehensive view of the nonlinear kinetic parameter values for four distinct kinetic models used during neem oil extraction process. These models include parabolic diffusion model, Elovich’s model, hyperbolic model, and power law. The values were obtained from testing at different temperatures and particle sizes, using hexane as the extraction solvent. This data is crucial in understanding the chemical kinetics involved in the extraction process and can be used to optimize extraction conditions for maximum efficiency [28, 36].

It was observed that the parameters C₁ and C₂ of the hyperbolic model exhibit an inverse relationship with increasing particle size, but a proportional relationship with temperature. The experiment showed that increasing temperature and decreasing particle size resulted in an increase in oil yield, which is attributed to the corresponding increase in C₁ and C₂. The trend observed in C₁ and C₂ across different temperature and particle size regimes indicates a high initial rate and total oil recovery at high temperature and smaller particle sizes. This observation is consistent with a study on the kinetic and parametric investigations of the extraction of jatropha oil by John et al. [22, 28]. Furthermore, the predicted oil yields from the models showed negligible differences from the experimental values.

Elovich kinetic model, power law, and parabolic diffusion models display a comparable pattern similar to the hyperbolic model. As the temperature and particle size decrease, the parameters of these models; A₁, A_o, B, E₁, and E_o, consistently increase. The experiment’s findings indicate that the power law model’s parameters, n and B, vary inversely with particle size and directly with temperature. Additionally, the parameter values of C₂, A₁, and E_o were lower than those of the hyperbolic, parabolic, and Elovich model’s parameter values of C₁, A_o, and E₁, respectively. This outcome is consistent with the outcomes reported by various studies, including Kitanovic et al. [20], Agu et al. [37], Menkiti et al. [35, 38, 39], and Teoh and Don  [40]. Agu et al. [37] studied the solvent extraction of Colocynthis vulgaris shrad seeds oil (CVSSO) using various solute to solvent ratios and observed a similar pattern of results. Similarly, Kitanovic et al. [20] investigated the solvent extraction of resinoid from the aerial part of Hypericum perforatum L using different solute to solvent ratios. Menkiti et al. [35, 38, 39], conducted studies on the kinetics of oil extraction from different plant materials, including mahogany seed, jatropha seed, and the leaf of Moringa oleifera, using different solvents. These studies also reported similar results, indicating that the kinetic model parameters varied inversely with particle size and directly with temperature. In summary, this study showed that the kinetic model parameters exhibit a consistent pattern of variation with particle size and temperature. Future experiments investigating the extraction of neem oil using hexane as a solvent can use these findings as a reference [4, 41].

Based on the results of the study, the C₂ values were slightly higher than what the authors had previously reported, while the C₁ values were slightly lower compared to other studies conducted by Agu et al. [37] and Menkiti et al. [35, 38, 39]. However, it is noteworthy that C₁ and C₂ values obtained in this study were similar to those reported by Kadurumba et al. [42] in their research on the solvent extraction of oil from Colocynthis vulgaris shrad (melon) seeds, even when different temperature and particle size variations were considered. The differences in the initial rapid oil extraction rates and final slow diffusion rate actions for oil extraction from different seeds, as reported by various authors, may explain the variations in the higher or lower values of C₁ and C₂. This suggests that the differences in the ultimate slow rate yield and initial rapid rate yield reported by different authors may be attributed to early quick washing action and slow diffusion-controlled regimes, respectively [4, 41].

Based on this study, it can be concluded that the power law model’s parameter, n, had a direct correlation with particle size variation. However, it did not exhibit a clear pattern when subjected to different temperature variations. The models indicated a better yield of extracted oil, which is attributed to the prevalence and effectiveness of the diffusion rate over the washing mechanism. Various studies, including Agu et al. [37], Menkiti et al. [43], and John et al. [22, 28], consistently showed an increase in kinetic parameter values with temperature. The oil yield was observed to rise steadily as the kinetic parameters decreased with smaller particle sizes. This is due to the larger surface area of smaller particles, allowing for a higher rate of mass transfer and oil dissolution in solvent. Additionally, the extraction rate of oil from neem oilseeds was faster at smaller particle sizes due to the reduced diffusion path [4, 41].

3.5.

Comparative results of statistical degree of fitness for kinetics models

In this section, we present the statistical degree of fitness for various nonlinear kinetic models that were evaluated for neem oil extraction using hexane as the extraction solvent. The criteria used to determine the best-fit kinetic model were R², SSE, Adj-R², and RMSE. Previous studies, conducted by John et al. [22–24, 28] and Mortazavian et al. [41], have noted that higher values of R² and Adj-R² and lower values of RMSE and SSE indicate a better fit of the model to the experimental data. Table 4 displays the statistical degree of fitness results for four kinetic models; parabolic diffusion, hyperbolic, Elovich’s model and power law. Results provide valuable insights to determine the most suitable model for neem oil extraction [24, 28, 41].

Based on the findings presented in Table 4, it can be inferred that an increase in temperature resulted in a decrease in SSE and RSME values, while the R² and adjusted-R² values demonstrated a direct correlation with temperature for power law, Elovich, parabolic, and hyperbolic models. This pattern indicates that these models have a superior ability to account for the overall variability in the data around the average, and that oil recovery improves as temperature and particle size decrease. The lower SSE and RSME values and higher R² and adjusted-R² values at higher temperatures and smaller particle sizes suggest a greater oil yield [4].

Furthermore, the declining SSE and RSME trend observed for the nonlinear kinetic models suggests that these models are more practical and advantageous for generating predictions related to oil recovery. Overall, these results imply that nonlinear kinetic models are more effective at predicting oil yield and can be considered a dependable tool in the oil industry [4, 41].

The hyperbolic, parabolic, Elovich, and power law models have shown impressive performance based on average SSE (≤8.4) and RMSE (≤0.76) values. In addition, the predicted R² and Adj-R² values for these models have ranged from ≥93% to ≤98% with R² and Adj-R² values for parabolic model showing the highest values and the hyperbolic model showing the lowest values (parabolic: 0.982, 0.976; power law: 0.979, 0.971; Elovich: 0.964, 0.951; hyperbolic: 0.930, 0.907).

It is evident from that nonlinear kinetic models: parabolic, hyperbolic, power law, and Elovich, exhibited a great degree of conformity to the experimental data. These models were evaluated based on the average SSE, RMSE, R², and Adj-R² values, and it was found that the hyperbolic model had the lowest degree of fitness, while the power law and parabolic models were the best fit for the experimental data. Notably, these two models had the lowest average SSE and RMSE values, and the highest R² and adj-R² values. The goodness of fit for the kinetic models to the experimental data was ranked in the following order: hyperbolic, Elovich, power law, and parabolic.

3.6.

Thermodynamics parameters

The data presented in Table 5 provides valuable insights into the thermodynamic parameters and equilibrium constant for the neem seed oil extraction process using hexane. Figure 3 provides a comprehensive overview of the In K versus 1∕T plots for different particle sizes 0.1, 0.3, and 0.45 mm, which were instrumental in determining the thermodynamic parameter values. It is interesting to note that the enthalpy values calculated for the oil extraction process varied depending on the particle size, ranging from 35.10 to 29.35 kJ/mol. When ethanol was used as a solvent to extract oil from Jatropha curcas L., the enthalpy values obtained in this study were found to be higher than those previously published by Silmara et al. [44], which ranged from 14.27 to 18.60 kJ/mol. Additionally, Meziane and Kadi [45] noted a lower enthalpy value (4–13.5 kJ/mol) for olive cake oil. These insights provide a valuable foundation for future research in this area.

The observed difference in the enthalpy values for the oil extraction process could potentially be explained by the various morphologies of the seeds, which could have an impact on the extraction process. It is worth noting that the extraction process is an endothermic process, as indicated by the positive enthalpy value. Therefore, an external energy input is required for an effective extraction process, as highlighted in studies by Silmara et al. [44], John et al. [23, 24], and Sulaiman et al. [32].

It is also worth mentioning that the obtained enthalpy findings are in agreement with the values published by Amin et al. [34] and Rodrigues et al. [46] for the extraction process of soybean oil using renewable solvent and the extraction of Jatropha curcas oil in aqueous acidic hexane solutions, respectively. These findings suggest that the enthalpy values of the oil extraction process are affected by factors such as the solvent used, the seed morphology, and the extraction method. These insights provide a valuable foundation for further research in this area, which could help optimize the oil extraction process and improve industrial practices [4, 5].

The positive differential entropy values obtained in all instances indicate that the oil extraction process is irreversible and the propensity of molecular breakdown is accelerated during the extraction procedure. The underlying cause of a disturbance observed during the extraction process is the mixing of two divergent materials or substances, as noted in studies by Silmara et al. [44], John et al. [23, 24],  and Sulaiman et al. [32]. These observations align with findings reported by several researchers, including Meziane and Kadi [45], Sayyar et al. [25], Liauw et al. [47], Amin et al. [34], Sulaiman et al. [32], Perez et al. [27], Topallar and Geçgel [48], Kostić et al. [49], and Silmara et al. [44] for various oilseed raw materials. By gaining a better understanding of the underlying causes of the extraction process disturbance, researchers could develop more sustainable and efficient extraction methods, leading to significant cost savings and environmental benefits [3–5].

The results of the study revealed that the entropy values of neem oil extraction process, using hexane-based method, ranged between 0.12 to 0.09 kJ/mol. These findings indicate that the extraction process is irreversible and is due to the extraction of oil molecules. Moreover, the mixture entropy values remained consistently positive throughout the extraction process, further supporting the irreversibility of the process.

The study’s results are consistent with the observations of Meziane and Kadi [45], Topallar and Geçgel [48], and Silmara et al. [44], who reported similar entropy values for oil extraction process. These observations have been confirmed by other researchers, indicating a general consensus on the irreversibility of the oil extraction process [4, 5].

Results of this study have shown that the oil extraction process had a negative Gibb free energy change (𝛥G°), indicating that the process was feasible and spontaneous under the experimental conditions examined. These findings are consistent with the observations of Sulaiman et al. [32], Agu et al. [37], Menkiti et al. [35], and Silmara et al. [44], who reported similar results.

Thermodynamic analysis revealed that the process required less energy to break bonds than is produced during solid–liquid interaction [32, 44]. Findings also indicate that the process becomes less spontaneous as particle sizes increase, which is consistent with the observations of Silmara et al. [44], John et al. [23, 24], and Sulaiman et al. [32].

In conclusion, the study’s results indicate that the oil extraction process is highly feasible and spontaneous under the examined experimental conditions. The findings of other researchers support this conclusion. The thermodynamic analysis provides valuable insights into the energy requirements of the process, highlighting the importance of particle size in optimizing the process. The study offers a valuable starting point for further research aimed at optimizing oil extraction process.

3.7.

Diffusion coefficients, activation energy, and mechanisms analysis

This section presents a comprehensive analysis of the diffusion coefficients, activation energy, and the underlying mechanisms of neem oil extraction using hexane as a solvent. The study addresses the dependence of diffusion on key process variables, such as temperature and particle size, determining the underlying extraction mechanisms, identifying the limiting steps, and delves into the extraction kinetics to establish predictive models that can optimize the process for industrial applications. Furthermore, it contrasts the findings with relevant literature to highlight advancements and identify possible research gaps. Understanding these thermodynamic and kinetic principles is critical for improving the extraction efficiency of neem oil, a promising second-generation feedstock for sustainable applications.

Diffusion coefficients (D) represent a fundamental parameter in modeling mass transfer during oil extraction process. In this study, the diffusion coefficients were determined by applying Fick’s second law of diffusion, which is often used in systems where mass transfer is governed by concentration gradients. The spherical particle model, typically used for oilseed extraction, assumes that diffusion occurs from the interior of the particles to the surrounding solvent.

The diffusion equation applied for neem oil extraction is expressed as:

where: Y_(t) is the oil yield at time t, Y_(∞) is the maximum oil yield (at equilibrium), D is the diffusion coefficient, r is the particle radius, and t is the extraction time.

From the experimental data, the diffusion coefficients were calculated for different temperatures and particle sizes by fitting the yield data to Equation (16). The results, presented in Table 6, indicate the dependence of diffusion coefficients on temperature and particle size.

The results show a clear relationship between diffusion coefficient and temperature, where higher temperatures lead to increased diffusion rates. This behavior can be attributed to enhanced molecular mobility and reduced viscosity of the solvent at elevated temperatures, which facilitates faster oil diffusion from the neem oilseeds into the solvent [13]. Conversely, as particle size increases, the diffusion coefficient decreases. Smaller particles present a larger surface area for mass transfer, enabling more rapid oil extraction. This trend is consistent with findings from other studies on oilseed extraction processes, such as Jatropha and olive cake oil extraction [10]. These findings align with studies in which temperature and particle size have been shown to be critical factors influencing the diffusion process during oil extraction [11, 14].

The activation energy (E_a) represents the minimum energy required for oil extraction process to proceed. Using the Arrhenius equation (Equation (17)), the activation energy was calculated by plotting the natural logarithm of the diffusion coefficient (In D) against the inverse of temperature :

where: D₀ is the pre-exponential factor, E_a is the activation energy, R is the gas constant (8.314 J/mol⋅K), and T is the absolute temperature (K).

The resulting plot yielded a straight line, with the slope providing the value of E_a. The activation energy for neem oil extraction was found to be 24.7 kJ/mol, as shown in Table 7. This relatively low activation energy suggests that the extraction process is efficient and requires moderate energy input and is largely driven by the diffusion mechanism. When compared to other oilseeds, such as Jatropha (25–35 kJ/mol) and soybean (30–40 kJ/mol), the activation energy of neem oil extraction falls in the lower range, indicating that it is a feasible process at moderate temperatures [11].

The pre-exponential factor (D₀) represents the diffusion coefficient at infinite temperature, and the value obtained in this study is consistent with those reported in other studies on biobased oil extraction [12]. The moderate activation energy further supports the notion that temperature plays a key role in enhancing the diffusion of neem oil, thus making the process energy-efficient, especially when performed at optimized conditions.