# Evaluation of the Total Organic Carbon (TOC) Using Different Artificial Intelligence Techniques

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}.

^{3}, R is the ratio of the organic matter to organic carbon as the weight percentage, ${\rho}_{mi}$ denotes the grain and pore fluid average density in g/cm

^{3}.

_{baseline}denote the evaluated formation and the base formation resistivity in ohm.m, Δt and Δt

_{baseline}represent the evaluated formation and base formation sonic transit times both in µs/ft, and LOM is the level of maturity.

_{o}) or T

_{max}instead of LOM, which simplify the use of Wang et al. [12] models, since the conversion between (T

_{max}or R

_{o}) and LOM is not required. Therefore, it reduces the practical problems [17]. Equations (5) and (6) are the revised ΔlogR models based on sonic and density logs, respectively. Equation (7) could be used to estimate the TOC using ΔlogR and gamma-ray log:

_{m}denotes the matrix sonic transit time (μs/ft), m represents the cementation exponent, ${\rho}_{m}$ and ${\rho}_{baseline}$ are the matrix and baseline densities (g/cm

^{3}), where the baseline density corresponds to R

_{baseline}value, α, β, δ and η are the matrix constants, which are different for different formations and must be determined, T

_{max}is the maturity indicator (°C), GR

_{baseline}is the baseline value of shale (API).

^{2}) of more than 0.92 compared with R

^{2}of 0.82 when the original ΔlogR model is used.

#### Different Applications of Artificial Intelligence Techniques

## 2. Methodology

#### 2.1. Experimental Testing Using Rock-Eval 6

_{2}, and CO. After that, the weight percentages of the residual carbon and oxidized mineral-carbon in every sample were determined by burning them in the oxidation oven at 300 °C for 30 seconds, then increasing the temperature up to 850 °C at a rate of 25 °C/min, and finally keeping the temperature at 850 °C for five minutes. More details about sample preparation procedures and considerations for TOC measurement by Rock-Eval 6 were reported by different authors [38,39,40].

#### 2.2. Proposed Methodology

^{2}) and correlation coefficient (R) between the predicted and the core measured TOC are obtained. The trained and optimized AI models were then tested using another set of data from the same well, and validated using data points collected from the Devonian shale formation. TOC predictability of the developed AI models for the validation data collected from Devonian formation was then compared with that of Wang et al. [12] sonic- and density-based models summarized in Equations (5)–(7).

#### 2.3. Data Description and Preprocessing

#### 2.4. AI Model’s Development

#### 2.5. Evaluation Criterion

#### 2.6. Application Examples to Barnett and Devonian Shale

## 3. Results and Discussion

#### 3.1. Training the AI Models

^{2}= 0.937, then M-FIS model with R

^{2}= 0.926, followed by FNN model with R

^{2}= 0.876, and finally SVM with the lowest R

^{2}of 0.871.

#### 3.2. Testing the AI Models

^{2}equal 0.870, 0.867, 0.842, and 0.818 for M-FIS, SVM, TSK-FIS, and FNN models, respectively.

#### 3.3. Validating the AI Models

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

AI | Artificial Intelligence |

AAPE | Average Absolute Percentage Error |

DR | Deep Resistivity |

DT | Sonic Transit Time |

FNN | Functional Neural Network |

FWB | Fort Worth Basin |

GR | Gamma Ray |

M-FIS | Mamdani Fuzzy Inference System |

RHOB | Formation Bulk Density |

SVM | Support Vector Machine |

TCF | Trillion Cubic Feet |

TSK-FIS | Takagi-Sugeno-Kang Fuzzy Inference System |

WCSB | Western Canada Sedimentary Basin |

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**Figure 2.**The relative importance of the data used to train (

**a**) Takagi-Sugeno-Kang fuzzy interference system (TSK-FIS), (

**b**) Mamdani fuzzy interference system (M-FIS), (

**c**) functional neural network (FNN), and (

**d**) support vector machine (SVM) models.

**Figure 3.**Comparison of measured and estimated TOC using (

**a**) TSK-FIS, (

**b**) M-FIS, (

**c**) FNN, and (

**d**) SVM for the training data sets.

**Figure 4.**Cross-plot of the measured and estimated TOC using (

**a**) TSK-FIS, (

**b**) M-FIS, (

**c**) FNN, and (

**d**) SVM for the training data set.

**Figure 5.**Comparison of measured and estimated TOC using (

**a**) TSK-FIS, (

**b**) M-FIS, (

**c**) FNN, and (

**d**) SVM for the testing data sets.

**Figure 6.**Cross-plot of the measured and estimated TOC using (

**a**) TSK-FIS, (

**b**) M-FIS, (

**c**) FNN, and (

**d**) SVM for the testing data sets.

**Figure 7.**Comparison of measured and estimated TOC using (

**a**) TSK-FIS, (

**b**) M-FIS, (

**c**) FNN, (

**d**) SVM, (

**e**) WSBM, and (

**f**) WDBM for the validation data sets.

**Table 1.**Statistical features of the data used to train the Takagi-Sugeno-Kang fuzzy interference system (TSK-FIS), Mamdani fuzzy interference system (M-FIS), functional neural network (FNN), and support vector machine (SVM) models.

Takagi-Sugeno-Kang Fuzzy Inference System | |||||

Data points = 545 | DR, Ωm | DT, μs/ft | GR, API | RHOB, g/cm^{3} | TOC, wt% |

Minimum | 4.97 | 50.95 | 23.73 | 2.39 | 0.75 |

Maximum | 163.3 | 97.1 | 146.9 | 2.7 | 5.1 |

Range | 158.3 | 46.1 | 123.2 | 0.3 | 4.4 |

Standard Deviation | 40.86 | 9.27 | 24.91 | 0.07 | 1.03 |

Sample Variance | 1670 | 86 | 621 | 0.0055 | 1.061 |

Mamdani Fuzzy Inference System | |||||

Data points = 545 | DR, Ωm | DT, μs/ft | GR, API | RHOB, g/cm^{3} | TOC, wt% |

Minimum | 4.97 | 53.78 | 28.07 | 2.39 | 0.76 |

Maximum | 163.3 | 95.0 | 146.9 | 2.7 | 5.0 |

Range | 158.3 | 41.2 | 118.9 | 0.3 | 4.2 |

Standard Deviation | 38.95 | 8.24 | 22.31 | 0.07 | 0.98 |

Sample Variance | 1517 | 68 | 498 | 0.0053 | 0.953 |

Functional Neural Network | |||||

Data points = 587 | DR, Ωm | DT, μs/ft | GR, API | RHOB, g/cm^{3} | TOC, wt% |

Minimum | 4.97 | 52.00 | 26.16 | 2.40 | 0.84 |

Maximum | 163.6 | 97.1 | 146.9 | 2.7 | 5.1 |

Range | 158.6 | 45.1 | 120.8 | 0.3 | 4.3 |

Standard Deviation | 42.12 | 7.52 | 20.73 | 0.06 | 0.85 |

Sample Variance | 1774 | 57 | 430 | 0.0040 | 0.731 |

Support Vector Machine | |||||

Data points = 671 | DR, Ωm | DT, μs/ft | GR, API | RHOB, g/cm^{3} | TOC, wt% |

Minimum | 4.97 | 50.95 | 27.37 | 2.39 | 0.76 |

Maximum | 163.6 | 97.1 | 146.9 | 2.7 | 5.1 |

Range | 158.6 | 46.1 | 119.6 | 0.3 | 4.4 |

Standard Deviation | 39.81 | 8.20 | 21.63 | 0.07 | 0.96 |

Sample Variance | 1585 | 67 | 468 | 0.0044 | 0.916 |

Takagi-Sugeno-Kang Fuzzy Inference System | |

Training/Testing Data Ratio | 65/35 |

Number of Membership Functions | 2 |

Input Membership Function | Gaussian Membership Function |

Output Membership Function | Linear Function |

Mamdani Fuzzy Inference System | |

Training/Testing Data Ratio | 65/35 |

Cluster Radius | 0.35 |

Number of Iterations | 300 |

Functional Neural Network | |

Training/Testing Data Ratio | 70/30 |

Training Method | Backward-Forward Selection Method |

Function Type | Non-linear Function with Iteration Terms |

Support Vector Machine | |

Training/Testing Data Ratio | 80/20 |

Kernel | gaussian |

Kerneloption | 9 |

Lambda | 1 × 10^{−7} |

Epsilon | 0.5 |

Verbose | 0.7 |

C | 3000 |

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## Share and Cite

**MDPI and ACS Style**

Mahmoud, A.A.; Elkatatny, S.; Ali, A.Z.; Abouelresh, M.; Abdulraheem, A.
Evaluation of the Total Organic Carbon (TOC) Using Different Artificial Intelligence Techniques. *Sustainability* **2019**, *11*, 5643.
https://doi.org/10.3390/su11205643

**AMA Style**

Mahmoud AA, Elkatatny S, Ali AZ, Abouelresh M, Abdulraheem A.
Evaluation of the Total Organic Carbon (TOC) Using Different Artificial Intelligence Techniques. *Sustainability*. 2019; 11(20):5643.
https://doi.org/10.3390/su11205643

**Chicago/Turabian Style**

Mahmoud, Ahmed Abdulhamid, Salaheldin Elkatatny, Abdulwahab Z. Ali, Mohamed Abouelresh, and Abdulazeez Abdulraheem.
2019. "Evaluation of the Total Organic Carbon (TOC) Using Different Artificial Intelligence Techniques" *Sustainability* 11, no. 20: 5643.
https://doi.org/10.3390/su11205643