# Data-Driven Analyses of Low Salinity Waterflooding in Carbonates
## 3 Results and Discussion
### Effect of LSW Governing Parameters on Oil Recovery
#### 3.1.2 Nonlinear Multivariable Regression  
Linear regression analysis did not show acceptable results to explain the relationship between governing parameters and the LSW effect. The strengths of the relationships from the multivariable linear regression model for different sets of variables were found to be from negligible to weak. Hence, no linear relationship between parameters and RF was established. We applied ML approaches and nonlinear regression models to further analyze these parameters. Data analyses were conducted using three different ML models: SVM, ANN, and DT. The random division of data points was achieved by separating them into training and testing groups, in the proportion of 0.7 to 0.3. Average correlation coefficients were obtained from 5000 simulations. The best-fit model was found to interpret the LSW performance.  
Oil/brine parameters were analyzed in this section. Different models and average coefficients of correlation obtained from three ML techniques are shown in Table 7. The best interpretation of LSW flooding based on brine parameters was achieved by DT with a minimum leaf size of 10, and the correlation coefficients for training and testing data are the highest among all ML models. A set of oil/brine properties, including dimensionless brine parameters and AN, were analyzed based on 42 data entries. All three ML models showed strong and very strong relationships between oil/brine parameters and RF; the data was a better fit than the case with only brine parameters. For brine properties, DT provided the best fit, as the average values of R are considered to be strong and moderate for training and testing data, respectively. For oil/brine parameters, ANN showed the highest training results for average R (0.75) but overfitted the testing data. DT yielded high correlation coefficients (0.68 for training and 0.63 for testing) with negligible overfitting, exhibiting good performance. Figures 4 and 5 show predicted RF values from the DT model and actual RF values for brine and oil/brine parameters. The average values and ranges of R, obtained from 5000 simulations, are illustrated in Figures 4 and 5. Table 8 shows the strengths of nonlinear relationships for these ML models.  
Figure 3: Predicted RF from linear regression and actual RF from experiments for oil/brine parameters (Predicted RF = 0.023 – 0.158 – DC – 0.0058 – AB + 0.091 – DTDS – 0.48 – DS).  
Figure 4: Predicted RF from DT and actual RF from experiments for brine parameters.  
Figure 5: Predicted RF from DT and actual RF from experiments for oil/brine parameters.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Number of** & \multirow{2}{*}{**Model**} & **Average R for** & **Average R for** \\  & **Data Points** & & **Training Data** & **Testing Data** \\ \hline \multirow{3}{*}{DC + DS + DTDS} & \multirow{3}{*}{96} & ANN & 0.20 & 0.04 \\  & & SVM & 0.24 & 0.18 \\ \cline{1-1}  & & DT & 0.57 & 0.35 \\ \cline{1-1}  & & ANN & 0.75 & 0.59 \\ \cline{1-1}  & & SVM & 0.73 & 0.61 \\ \cline{1-1}  & & DT & 0.68 & 0.63 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The results obtained from three ML models for different sets of parameters.  
Using linear regression, we showed that the LSW effect could not be modeled based on a single parameter, it is the result of combined contributions by several parameters. Therefore, we made predictions of LSW based on a set of main parameters and discovered that the best prediction was made using oil/brine properties. ML models helped us to achieve better results in explaining the connection between a set of controlling parameters and the incremental RF by LSW flooding.