# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 3 Selection, Processing, and Correlation Analysis of Training Samples
### Construction, Evaluation, Comparison, and Application of the Two Approaches
Furthermore, the Approach 1 model outperforms the Approach 2 model across all three evaluation metrics. In contrast, the Approach 1 model achieves impressively low values for MSE and MAE, specifically 0.000229935 and 0.011198329, respectively, whereas the Approach 2 model experiences a significant escalation in MSE and MAE, soaring by 992.393% and 240.674%, respectively, compared to the Approach 1 model. Additionally, the Approach 1 model attains an impressive R\({}^{2}\) value of 0.92178272, whereas the Approach 2 model lags behind with a value of merely 0.552230669, resulting in a substantial difference of 66.920% between the two models and underscoring the superior accuracy of the Approach 1 model. The analysis above leads to the conclusion that the inclusion of formation density as an input parameter, despite lacking a direct correlation with formation pressure loss from a single data correlation perspective, is still relevant in terms of its physical significance and does not compromise the prediction accuracy of the model. Conversely, it narrows down the range of relative errors and diminishes the occurrence of extreme prediction values. Figure 11: The performance of the two scheme models on the test set. Figure 12: Comparison diagram of equivalent density of leakage pressure predicted by two schemes of the M-2 well model. (**a**) The layered profile of the predicted value of the formation leakage pressure of the two schemes of the model in Well M-2 is plotted. (**b**) The vertical profile of the whole well section of the predicted value of the formation leakage pressure of the M-2 well is plotted. (**c**) The cross-plot of the calculation results of the formation leakage pressure formula method of Well M-2 and the prediction results of the LSTM-BP model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Formation**} & \multirow{2}{*}{**Well Depth**} & \multicolumn{6}{c}{**Predicted Value of Equivalent Density of Leakage Pressure (g/cm\({}^{3}\))**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Scheme 1**} & \multicolumn{2}{c}{**Scheme 2**} & \multicolumn{2}{c}{**Calculation Formula Method**} \\ \cline{3-8}  & & \multicolumn{1}{c}{**Minimum**} & \multicolumn{1}{c}{**Maximum**} & \multicolumn{1}{c}{**Minimum**} & \multicolumn{1}{c}{**Maximum**} & \multicolumn{1}{c}{**Minimum**} & \multicolumn{1}{c}{**Maximum**} \\ \hline B & 2510–3014 & 1.587 & 1.689 & 1.618 & 1.679 & 1.570 & 1.705 \\ C1 & 3014–3569 & 1.584 & 1.700 & 1.612 & 1.675 & 1.582 & 1.718 \\ C2 & 3569–3854 & 1.584 & 1.711 & 1.619 & 1.680 & 1.593 & 1.722 \\ D & 3854–4790 & 1.589 & 1.905 & 1.617 & 1.909 & 1.590 & 1.952 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The equivalent density range of predicted leakage pressure in different layers of two schemes of M-2 well model. The results demonstrate that both approach models effectively capture the overall trend of the formation pressure loss equivalent density in the M-2 well, exhibiting consistent predictions across most depth intervals. In comparison to the Approach 1 model, the Approach 2 model exhibits relatively smoother predictions and performs similarly, apart from a slight tendency to overestimate in the middle and lower sections of the D Formation. Since the actual formation pressure loss values are unavailable for the M-2 well, and direct validation of the models' predictions is not possible, the calculated formation pressure loss values obtained using Equation (2) were compared to the predictions generated by the Approach 1 and Approach 2 models, serving as a point of reference for evaluation purposes. Table 4 presents the drilling fluid density utilized throughout the drilling process of the M-2 well. Importantly, there were no wellbore losses during the drilling of the M-2 well, and a formation leak-off test conducted at a depth of 3768 m confirmed the absence of formation leakage. Consequently, the lack of actual formation pressure loss data prevents the validation of the predictions made by the two approach models.