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14 November 2022

Predicting Enthalpy of Combustion Using Machine Learning

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1
Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
2
Center for Refining and Advanced Chemicals, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
3
SDAIA-KFUPM Joint Research Center for Artificial Intelligence, Dhahran 31261, Saudi Arabia
4
Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Processes2022, 10(11), 2384;https://doi.org/10.3390/pr10112384
This article belongs to the Special Issue Application of Artificial Intelligence (AI) in Chemical Science and Engineering
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Abstract

The present work discusses the development and application of a machine-learning-based model to predict the enthalpy of combustion of various oxygenated fuels of interest. A detailed dataset containing 207 pure compounds and 38 surrogate fuels has been prepared, representing various chemical classes, namely paraffins, olefins, naphthenes, aromatics, alcohols, ethers, ketones, and aldehydes. The dataset was subsequently used for constructing an artificial neural network (ANN) model with 14 input layers, 26 hidden layers, and 1 output layer for predicting the enthalpy of combustion for various oxygenated fuels. The ANN model was trained using the collected dataset, validated, and finally tested to verify its accuracy in predicting the enthalpy of combustion. The results for various oxygenated fuels are discussed, especially in terms of the influence of different functional groups in shaping the enthalpy of combustion values. In predicting the enthalpy of combustion, 96.3% accuracy was achieved using the ANN model. The developed model can be successfully employed to predict the enthalpies of neat compounds and mixtures as the obtained percentage error of 4.2 is within the vicinity of experimental uncertainty.

1. Introduction

Thermochemistry is a subfield of chemical thermodynamics that studies the interactions of heat, work, and other forms of energy in the context of chemical and physical processes. When a system undergoes a change of state, its internal energy, enthalpy, and associated properties change to account for the energy transfer between the system and the surroundings. All heat engines around us, including steam power plants, gas power plants, and automobiles, operate by converting the chemical energy of the fuel into thermal energy, which is subsequently converted to the desired end-use form. In this regard, the enthalpy of combustion is defined as the quantum of change in enthalpy when any element/compound undergoes complete oxidation at a given temperature and pressure. Enthalpies of combustion for various substances are typically measured using a bomb calorimeter (see Figure 1). However, measuring the enthalpy of combustion of various fuels, fuel blends, and surrogates is a time-consuming and costly procedure which necessitates the use of alternate approaches. Among the various possible approaches, the use of machine learning to predict the enthalpy of combustion is promising and has been explored extensively in this work.
Figure 1. A cross-sectional view of typical bomb calorimeter.
Machine-learning tools help in predicting the enthalpy of combustion for various fuels once they have been rigorously tested over a predefined dataset. A number of machine-learning algorithms have been developed over the years, such as decision trees, random forests, Naïve Bayes, support vector machines, k-means, etc. Neural networks are a subset of machine learning and are at the heart of deep learning algorithms. Typical machine-learning methods are based on the use of neural networks with one or more layers connecting the desired output to the given input. A neural network is a set of algorithms that attempts to detect underlying relationships in a piece of data using a technique similar to the way that the human brain works. In this context, neural networks are systems of neurons that might be biological or artificial in origin. Due to their excellent adaptability to changing inputs, neural networks are widely being used to obtain the best possible results without the need to change the output criterion. Artificial neural networks (ANNs) have therefore been used in this study to develop the required machine-learning tools.
The use of ANNs for predicting the enthalpy of combustion is rather novel. The few relevant studies that have utilized multiple approaches for developing predictive models for the estimation of the enthalpy of combustion are discussed here. Gharagheizi et al. [1] developed an ANN-based model to predict the enthalpy of combustion of various pure compounds using the group-contribution method. A squared correlation coefficient of 0.99999 with a root-mean-squared error of 12.57 kJ/mol, in comparison with experimental values from the literature, was reported. Albahri [2] also used the group-contribution method for predicting the enthalpy of combustion; however, a multivariable nonlinear-regression-based method was used for this purpose. The enthalpy of combustion was predicted based on the molecular structure, with a reported average error of 0.71%. Recently, Dashti et al. [3] compared three different models, namely a least-squares support-vector machine, genetic programming, and an adaptive neuro-fuzzy inference system, for predicting the enthalpy of combustion of several chemical compounds. It was concluded that the particle swarm optimization–adaptive neuro-fuzzy inference system (PSO–ANFIS) model with four inputs was the most accurate among the three models. The ANFIS structure contains five layers: 1: the fuzzification layer; 2: the IF layer; 3: the normalization layer; 4: the THEN layer; and 5: the summation layer. In this model, MF variables should be estimated immediately after the generation of the initial FIS model and the training of the ANFIS. The MF values are adjusted via PSO algorithms to find the finest structure [3].
This study reports a detailed ANN model to predict the enthalpy of combustion of compounds (neat and mixtures) and real fuels belonging to different chemical families. The functional groups present in the fuels are used as input features to the ANN model. The method of using functional groups for predicting fuel properties has been reported in a number of recent studies [4,5,6]. Functional groups present in the fuels are also relevant for surrogate formulation [7], particulate matter formation [8,9,10,11], and property prediction [12,13,14].

2. Theoretical Background

The enthalpy of combustion is calculated using the data from the bomb calorimeter using Equation (1):
Δ H c = m × C p × Δ T
where ∆Hc is the enthalpy of combustion in kJ, m is the mass of water in kg, Cp is the specific heat capacity of water in kJ/kg °C, and ∆T is the temperature change of water in °C. After obtaining these enthalpies of combustion from the literature, each compound was defined with a specific variable according to a convention so that the machine could relate the given enthalpy of combustion to the corresponding compound. To define each compound, 13 variables were assigned to each compound. These variables, along with their definitions, are presented in Table 1.
Table 1. Variables, along with their definitions.
BI refers to the branching index of the molecule or mixture. It represents the degree of branching/linearity of a molecule, while including the impact of paraffinic branches on the longest chain present in the molecule. More information related to BI has been reported here [15,16].

3. Dataset and Machine Learning

The dataset was built using the collection of data from the extensive available literature on the enthalpy of combustion that meets the criteria that all data should be at the same condition (i.e., temperature and pressure) and that the method used to obtain these enthalpies should be consistent (i.e., bomb calorimeter method).
After the collection of all the possible data, Table 2 and Tables S1–S10 were generated. Tables S1–S10 are provided in the Supplementary Materials. Table 2 shows the enthalpy of combustion for 204 compounds from the literature. Edwards and Maurice (2001) [17], estimated the enthalpy of combustion for five surrogates (S1–S5), containing a total of 38 compounds, as shown in Table S1. Similarly, Huber et al. (2009) [18] reported the enthalpy of combustion for two surrogates (S6 and S7), consisting of a total of five compounds, as shown in Table S2. Table S3 represents the enthalpy of combustion for six surrogates (S8–S13), containing a total of five components, as studied by Shrestha (2014) [19]. Similarly, Kalghatgi et al. (2011) [20] calculated the enthalpy of combustion for three surrogates (S14–S16), containing a total of three compounds, as shown in Table S4. Table S5 shows the enthalpy of combustion for two surrogates (S17–S18), comprising a total of nine components, as studied by Huber et al. (2010) [21]. In a same way, Eddings et al. (2005) [22] estimated the enthalpy of combustion for two surrogates (S19–S20), containing a total of six compounds, as shown in Table S6. Table S7 shows the enthalpy of combustion for two surrogates (S21, S22), comprising a total of three fuel constituents, as studied by Naik et al. (2010) [23]. Grubinger et al. (2021) [24] estimated the enthalpy of combustion for three surrogates (S23–S25), containing a total of 11 compounds, as shown in Table S8. Similarly, Table S9 shows the enthalpy of combustion for 9 surrogates (S26–S34), containing a total of 17 compounds, as reported by Xu et al. (2015) [25]. Grubinger et al. (2021) [24] reported the enthalpy of combustion for four surrogates (S35–S38), containing a total of six compounds, as shown in Table S10.
Table 2. Enthalpy of combustion of different compounds from the literature.
Once the dataset had been built, the variables were used as inputs to the ANN were calculated. The procedure for the calculation of 11 variables for specific fuels/chemicals, as applied to a few examples, is available in our previous publications [15,16]. After defining all compounds and mixtures, all the definitions and the corresponding enthalpies were imported to MATLAB to yield a neural network with 14 input layers, 26 hidden layers, and 1 output layer. Finally, to obtain the ANN model for predicting the enthalpy of combustion, the model needed to be trained to study and evaluate the effects and the relationships between each of these variables. Some of these effects and relationship are presented in this study.

4. Results and Discussion

The data used for developing the model was obtained from the literature and imported into MATLAB. The impact of the functional groups on the enthalpy of combustion was evaluated by means of various plots. Figure 2, Figure 3, Figure 4 and Figure 5 show that the enthalpy of combustion increases with an increase in the weight percentage of the paraffinic CH2 groups present in various chemical classes of the fuels in the dataset. These groups represent the linearity of the hydrocarbon molecule and have been shown to have a significant impact on a number of combustion properties, such as the antiknock rating, ignition quality, flash point, etc.
Figure 2. The effect of weight percentage of CH2 on enthalpy of combustion for iso-paraffins.
Figure 3. The effect of weight percentage of CH2 on enthalpy of combustion for n-paraffins.
Figure 4. The effect of weight percentage of CH2 on enthalpy of combustion for blends.
Figure 5. The effect of weight percentage of CH2 on enthalpy of combustion for olefins.
However, increasing the weight percentage of olefins, alcohols, ketones, and aldehydes results in decreased enthalpy of combustion (see Figure 6, Figure 7, Figure 8 and Figure 9). However, these figures need to be considered carefully as an increase in the weight percentage of olefins is the result of increasing the CH2 percentage. Overall, increasing the molecular weight of a compound or a surrogate leads to the increased enthalpy of combustion, as shown in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17. Molecular weight has a significant impact on the physical properties of pure compounds and blends and is known to influence properties, including viscosity, density, and surface tension, and also phenomena, such as heating, vaporization, droplet formation, etc. Figure 18 shows the effect of the branching index on the enthalpy of combustion for all of the collected data. It can be clearly observed that, as the branching index increases, the enthalpy of combustion increases for all classes of compounds in the data. The branching index denotes the linearity/nonlinearity of a compound by considering the carbon framework of the compound. Inclusion of the branching index as an input feature has shown to reduce the error in prediction in a large number of studies.
Figure 6. The effect of weight percentage of CH-CH2 on enthalpy of combustion for olefins.
Figure 7. The effect of weight percentage of OH on enthalpy of combustion for alcohols.
Figure 8. The effect of weight percentage of CO on enthalpy of combustion for ketones.
Figure 9. The effect of weight percentage of CHO on enthalpy of combustion for aldehydes.
Figure 10. The effect of molecular weight of iso-paraffins on enthalpy of combustion.
Figure 11. The effect of molecular weight of n-paraffins on enthalpy of combustion.
Figure 12. The effect of molecular weight of naphthenes on enthalpy of combustion.
Figure 13. The effect of molecular weight of olefins on enthalpy of combustion.
Figure 14. The effect of molecular weight of ketones on enthalpy of combustion.
Figure 15. The effect of molecular weight of alcohols on enthalpy of combustion.
Figure 16. The effect of molecular weight of blends on enthalpy of combustion.
Figure 17. The effect of molecular weight of aldehydes on enthalpy of combustion.
Figure 18. The effect of branching index on enthalpy of combustion for all collected data.
Subsequently, a neural network model was created and trained in MATLAB, resulting in an overall accuracy of 96.3% (see Figure 19). A regression coefficient of 0.959 was obtained when the developed model was applied to the training data, indicating that the model was able to succeed in learning the impact of the input features on the target (i.e., the enthalpy of combustion). The model was validated with approximately 15% of the dataset and yielded a regression coefficient of 0.97. The final testing of the ANN code was performed using a test set that was randomly selected by the software. The measured and predicted enthalpy of combustion values for the 40 compounds of the test set are shown in Table 3. The average percentage error obtained was 4.2%, which is near the range of experimental error.
Figure 19. The best obtained result of training the dataset in a neural network.
Table 3. Comparison between the measured enthalpies and the predicted ones.

5. Conclusions

This study presents an ANN model with 14 input layers, 26 hidden layers, and 1 output layer to predict the enthalpy of combustion of various oxygenated fuels. The ANN model was built in the MATLAB environment, and it used a detailed dataset of enthalpy of combustion values from the literature. The model was trained, validated, and tested using enthalpy of combustion data for various compounds and fuel surrogates, including numerous chemical classes: paraffins, olefins, naphthenes, aromatics, alcohols, ethers, ketones, and aldehydes. The influence of various functional groups on the enthalpy of combustion has been illustrated graphically and discussed. The procedure for the development of the model has been explained in detail. The overall precision of the developed ANN model in projecting the enthalpy of combustion was approximately 96.3%, and the average percentage error of the model, when applied against the test set, was 4.2. This value is close to that of the experimental uncertainties observed when measuring the enthalpy of combustion. This supervised machine-learning model can be used to predict the enthalpies of pure compounds and real petroleum fuels.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/pr10112384/s1, Table S1. Enthalpy of combustion for surrogates Edwards & Maurice, 2001 [17], Table S2. Enthalpy of combustion for surrogates Huber et al. (2009) [18], Table S3. Enthalpy of combustion for surrogates Shrestha (2014) [19], Table S4. Enthalpy of combustion for surrogates Kalghatgi et al. (2011) [20], Table S5. Enthalpy of combustion for surrogates Huber et al. (2010) [21], Table S6. Enthalpy of combustion for surrogates Eddings et al. (2005) [22], Table S7. Enthalpy of combustion for surrogates Naik et al. (2010) [23], Table S8. Enthalpy of combustion for surrogates Grubinger et al. (2021) [24], Table S9. Enthalpy of combustion for surrogates Xu et al. (2015) [25], Table S10. Enthalpy of combustion for surrogates Grubinger et al. (2021) [24].

Author Contributions

Conceptualization, A.G.A.J. and A.A.-M.; methodology, A.G.A.J. and A.B.S.A.; software, A.A.-M. and U.A.; validation, A.G.A.J., A.A.-M. and A.B.S.A.; formal analysis, N.A. and U.Z.; investigation, A.A.-M.; resources, A.G.A.J.; data curation, U.Z. and U.A.; writing—original draft preparation, A.A.-M. and A.G.A.J.; writing—review and editing, N.A. and A.B.S.A.; visualization, N.A. and U.Z.; supervision, A.G.A.J. and U.A.; project administration, A.G.A.J. and A.B.S.A.; funding acquisition, A.G.A.J. All authors have read and agreed to the published version of the manuscript.

Funding

The work was funded by the Interdisciplinary Research Center for Refining & Advanced Chemicals (CRAC) at King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia, under the funded project INRC2104.

Data Availability Statement

Not applicable.

Acknowledgments

The authors would like to acknowledge the support received from the Interdisciplinary Research Center for Refining & Advanced Chemicals (CRAC) at King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia, under the funded project INRC2104.

Conflicts of Interest

The authors declare no conflict of interest.

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