# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 5 Conclusions  
1. In this study, an LSTM-BP intelligent prediction model was developed to estimate formation leak-off pressure, and both Scheme 1 and Scheme 2 were employed for evaluation. The results demonstrated a significant disparity in the performance of the three evaluation metrics between the Scheme 1 and Scheme 2 models throughout the training process. Notably, the Scheme 1 model exhibited commendable performance on both the training and testing sets, whereas the Scheme 2 model displayed inadequate performance. The Scheme 1 model achieved a remarkable reduction of 992.393% and 240.674% in MSE and MAE on the testing set, respectively, in comparison to the Scheme 2 model. Furthermore, it achieved a notable increase of 66.920% in R\({}^{2}\). The Scheme 1 model demonstrated a relative error range of (\(-\)2.467%, 2.510%) and (\(-\)6.141%, 5.201%) on the testing set, confirming the high prediction accuracy of the LSTM-BP model developed in this study. Moreover, incorporating formation density as an input variable, despite lacking a direct singular correlation with leak-off pressure, did not diminish the predictive accuracy of the model. In fact, it contributed to a narrower range of relative errors. 2. The LSTM-BP models, trained using Scheme 1 and Scheme 2, were employed to predict the formation leak-off pressure in the adjacent M-2 well. The outcomes demonstrated that the predicted values from both model schemes displayed comparable overall trends. Nevertheless, the majority of predicted outcomes from the Scheme 2 model fell within the prediction range of the Scheme 1 model, implying that the Scheme 1 model exhibited greater volatility in its predictions. Additionally, it was observed that the predicted outcomes of the Scheme 1 model closely aligned with the results derived from the formula method, whereas the Scheme 2 model exhibited noticeably inferior performance compared to the Scheme 1 model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**ML Models**} & \multirow{2}{*}{**Name**} & \multicolumn{5}{c}{**Evaluation Index**} \\ \cline{3-8}  & & **MAE** & **Difference (\%)** & **MSE** & **Difference (\%)** & **R\({}^{2}\)** & **Difference (\%)** \\ \hline Random & Scheme 1 & 0.012151 & 0.013233 & 8.172 & 0.0004350 & 15.825 & 0.833446 & 3.266 \\ forest & Scheme 2 & 0.013233 & 8.172 & 0.000504 & 15.636 & 0.405156 & 16.454 \\ BP & Scheme 1 & 0.027050 & 2.324 & 0.001746 & 15.636 & 0.405156 & 16.454 \\  & Scheme 2 & 0.027678 & 0.027678 & 0.001746 & 15.636 & 0.405156 & 16.454 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The performance of random forest and BP algorithms on the test set under the conditions of the two scheme models in the M-1 well. 3. The models were trained using the BP and random forest algorithms based on Scheme 1 and Scheme 2. The findings revealed that, irrespective of BP or random forest, the Scheme 1 models outperformed the Scheme 2 models on the testing set. These results suggest the generalizability of the conclusions drawn in this study to other algorithms. Additionally, it was noted that both the BP and random forest models exhibited inferior performance compared to the LSTM-BP model developed in this study, highlighting the superiority of the LSTM-BP model. 4. The prevention of wellbore losses poses a challenging problem in the field of oil and gas exploration and development. Wellbore losses involve intricate mechanisms, and controlling them requires consideration of multiple factors. Precisely predicting formation leak-off pressure plays a crucial role in effective control measures. The development of the LSTM-BP intelligent prediction model for formation leak-off pressure, which incorporates physical data and is driven by dual factors, represents a valuable contribution to the study of formation leak-off pressure and serves to advance the progress of intelligent drilling technology. Nevertheless, this study possesses certain deficiencies and constraints. For instance, the model's input layer solely incorporates well logging data.