The essential oil market is a well-established industry with interconnections with other industries, such as processed food, perfume fragrance, and strategic sectors (Maurya et al., 2021; Sharmeen et al., 2021; Israfi et al., 2022; Navarra et al., 2015; Bora et al., 2020). The world market has not yet recovered from the massive collapse of commerce during the COVID-19 pandemic and still shows signs of deceleration, with orange production dropping from the principal producers worldwide (Brazil, Florida, and Spain) (United States Department of Agriculture, 2022). Consequently, prices of citrus essential oils have reached unprecedented high levels (Technavio, 2022), making it attractive for newcomer producers to enter the market at least to cover local demand. The city of Las Naves in the Ecuadorian province of Bolivar is an attractive hub for citrus fruit production, with ambitious signs of expansion. Ecuador’s national institution for statistics and census (Instituto Nacional de Estadística y Censos—INEC) and the Ecuadorian minister’s office for agriculture and livestock farming (Ministerio de Agricultura y Ganadería—MAG) estimate a rise in orange production to 110.472 tons in upcoming years. At a local level (in other provinces in Ecuador), citrus fruit from Las Naves attracts high demand and consumption, guaranteeing a vast source of citrus waste that could ultimately serve in secondary product production.

Essential oils are organic compounds that provide the characteristic odor to citrus fruits and are a principal component of orange rind. The main component of citrus essential oil is limonene; its empirical formula (C₁₀H₁₆) is a monoterpene that exhibits two D- and L-limonene optical isomers and the racemic combination known as dipentene (González-Mas et al., 2019). Limonene is present in more than 49 volatile organic compounds (90% classified as terpenoid esters), with concentrations depending on the fruit variety: 30%–40% in bergamot, 40%–75% in lemon, and 68%–98% in sweet orange (Moufida and Marzouk, 2003). Most of its chemical and physical extraction processes rely on essential oil molecular volatility (Balboa Laura, 2011), although the quality and quantity of the essential oils in the fruit peel can impact the extraction efficiency levels independently of the extraction method (García, 2014). Microwave-assisted hydrodiffusion stands out because it is solvent-free and highly efficient with a short extraction time (Bustamante et al., 2016; Bora et al., 2020). However, for any extraction method, a highly accurate predictive model capable of determining extraction efficiency is very important for the optimization and design of scalable extraction pathways at various levels, such as in the laboratory or industry.

The wide set of variables and their non-linear and complex inter-relations make predicting the extraction yield of essential oil a challenging task. A lack of generality for mathematical models also contributes to this difficulty, with models being extraction technique-dependent (Berna et al., 2000; Sovová, 2005; Lainez-Cerón et al., 2022; El Ouaddari et al., 2022). A prediction model for steam distillation can even become obsolete with a variation in the essential oil source (Gawde et al., 2014). The inadequacy of a clear quality standard for a mathematical tool for predictions has led researchers to use polynomial, exponential, and logarithmic fitting tools to help at least with predictions in the locality (local space) of the data points (Zlatev and Shivacheva, 2018; Fakayode and Abobi, 2018). The local space of these basic fitting types comes at the expense of prediction capability away from the local domain—that is, extrapolation, a prediction feature required to enable the scalability of the extraction processes.

Artificial intelligence is a numerical approach that recognizes internal patterns in data to identify and classify data into larger sets. Artificial intelligent algorithms can then handle non-linearity and complexity in data structure and predict outputs of numerical processes (Meuwly, 2021). Given the complex nature of the variables in chemical processes, artificial intelligence is a suitable tool for formulating prediction models in this field. Steam distillation extraction models with artificial neural network algorithms have achieved remarkable accuracy in yield prediction of oil extraction from the soil (Daryasafar et al., 2014). Optimization of operating conditions in energy-intensive distillation processes can be explored via a machine learning-based predictive model concluding with recommendations for optimal steam flow that minimize energy consumption and maximize production yield (Park et al., 2022). We focus on developing an artificial intelligence model with a tool for steam distillation yield prediction of essential oil extraction from orange peel.

Using state-of-the-art artificial intelligence algorithms, this work introduces a technique-independent predictive neural network model for essential oil extraction from orange peel. We present a multi-layer perceptron (MLP) artificial neural network (ANN) with supervised learning. The model topological architecture achieves its best prediction via internal node adjusting of the model structure, while statistical error descriptors of the testing set are optimized. The MLP ANN handles input (orange peel mass) and output (essential oil mass) data from steam distillation experiments. Steam distillation is the most common technique at the laboratory level for essential oil extraction (Ferhat et al., 2006) and works on the principle that oil molecules diffuse when attached to water molecules in the vapor state (Chandler, 2002). The mean square error (MSE) and the coefficient of determination (R ²) are the error descriptors of choice to guide network optimization, as used elsewhere (Park et al., 2022). A single hidden layer with nine neurons, back-propagation, and neural weights adjusted using the Levenberg–Marquardt algorithms optimizes the MSE and R ² of the oil extraction model. This model approach paves the way for planning and designing oil extraction processes at larger scales than in the laboratory.

A homogeneous sample quality guaranteed enhanced statistical confidence in the data and thus improved the model’s prediction accuracy. We implemented a quality control scheme where, after the peel washing step described in Section 2, the regular peel chunks that fell within a 5% confidence interval relative to the standards in Table 1 were selected for the extraction experiments. High humidity was desirable so that an even molecular mixture (water + limonene oil molecules in the orange peel) would boil at lower boiling points than the separate liquids while steam flowed through the sample in the steam distillation experiments.

Figure 1 and Table 2 summarize the experimental results at 200 g, 300 g, 350 g, 400 g, and 500 g mass loading levels with the washed regular chunks of orange rind after the extraction treatment. Yield figures are comparable with literature reports for steam distillation of essential oil from C. sinensis peel (Blanco Tirado et al., 1995; de Moraes Pultrini et al., 2006).

As the mass loading increases, the extracted essential oil mass should linearly augment in the distillation process as depicted in Figure 1. However, the extraction yield scales up with the mass loading at a faster rate than the linear trend, rendering a positive over-extraction. This analysis is further supported by a principal analysis component developed in Section 2.5, with data increasing non-linearly with respect to the mass loading. This behavior makes the data structure ideal for non-linear numerical processes such as in the MLP algorithm. A t-distribution confidence interval analysis with 95% confidence and four degrees of freedom further supports the over-linear increase of the extraction yield. The t-distribution estimations (Column 4 in Table 2) suggest a more efficient extraction with sample weight.

Sun et al. (2017) also reported an over-linear dependency between the extraction yield and sample weight. Although the reason behind this dependency is beyond our current scope, we theorize that larger sample weights render an enhanced molecular diffusion across the orange peel–water interface. A larger loading mass occupies a larger space in the mass loading chamber, reducing the mixture’s boiling point (water vapor + essential oil molecules), thus promoting more material extraction. We will investigate this in more detail in subsequent research.

The MLP neural network shows promising results in Figure 2, predicting the extraction oil yield as a function of the neuron numbers for the 350-g sample set. Figure 2A shows the evolution of the error descriptors (MSE and R ²) while the number of neurons increases in the network’s hidden layer. R ² stabilizes after six neurons, reaching a plateau afterward, while MSE bounces during the neuron number increment. Figure 2B describes the evolution of the predicted values from the network given a denser hidden layer.

We observe a clear correlation between the MLP’s predictions in Figure 2B and MSE in 2A. Numerical analysis demonstrates the MSE’s correlation with the model predictions stems from the MSE’s sensitivity to spiking values in the MLP model. We define a spiking value as m ^pred falling into the range of more than three sigma errors about m ̄ exp . Conversely, although R ² exhibits some spiking behavior at low neuron numbers (Figure 2A), this error descriptor stabilizes as the neuron number increases, given the weighing denominator in Equation 2. While the neuron number increases, R ² compounds the effects of both the predicted and mean values of the sample weight sets, diluting any spiking behavior from the predicting algorithm. The different sensitivity levels to the statistical data of both R ² and MSE show the importance of utilizing more than one error descriptor during the network outcome optimization. The optimization process demonstrates that the optimal neuron number to use in the hidden layer is 9, based on two findings: a stable R ² and MSE and predictive values within the mean yield confidence interval for the 350 g set - 0.110 , 0.122 .

The predictive capacity of the network outperforms other more common mathematical models widely used in the literature (Zlatev and Shivacheva, 2018; Fakayode and Abobi, 2018), as observed in Table 3, with the highest R ² for the MLP neuron network. Our MLP model shows clear advantages over other models in accurately predicting the extraction yield for the 350-g mass loading set located in the vicinity of the sample weight range (from 200 to 500 g). With larger training sets, MLP should accurately predict the extraction values far from the training sample weight range. This feature is relevant for planning and designing scalable industrial extraction processes and is a valuable approach for initiating the leap from the laboratory to industrial scale-up.

We developed an innovative and alternative approach for an oil extraction yield predictor using state-of-the-art artificial intelligence algorithms. We use steam-distilled essential oil extraction data from orange peel to train a multi-layer perceptron (MLP) neural network in a supervised learning approach to achieve an accuracy beyond the standard predicting models in the literature. By simultaneously optimizing two fitting parameters (R ² and MSE), we demonstrate that the MLP neural network achieves its optimal architecture with one hidden layer and nine neurons, obtaining accuracy and predicting capabilities at R ² = 0.9929 and EMC% = 0.0040 for the validation sample set. The model developed in this work has the potential to unlock prediction capabilities in line with scalable design to bring lab-based production prototypes to an industrial level, thus being a viable path for a temporary solution for the citrus oil market.