# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 4 Conclusions  
This study describes the results of the development of data-driven proxy models to predict reservoir production performance for one cycle of steam huff and puff injection. The proposed models comprise 28 input parameters consisting of reservoir properties and operating designs, and 6 output parameters consisting of reservoir production and reservoir characterization parameters after the injection cycle. For each output parameter, a polynomial regression model and a neural network model were developed. Adjusted R-square, mean absolute error (MAE) and root mean squared error (RMSE) were used to evaluate the performance of all models. Based on the results of our study, the neural \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Proxy Model**} & \multicolumn{2}{c}{**Polynomial Regression**} & \multicolumn{2}{c}{**Neural Network**} \\ \cline{2-5}  & **Training R-Square** & **Testing R-Square** & **Training R-Square** & **Testing R-Square** \\ \hline \(N_{p}\) & 0.755 & 0.735 & 0.981 & 0.959 \\ \(q_{0 max}\) & 0.706 & 0.675 & 0.957 & 0.931 \\ \(q_{end}\) & 0.561 & 0.524 & 0.953 & 0.847 \\ \(p_{end}\) & 0.878 & 0.877 & 0.991 & 0.989 \\ \(T_{end}\) & 0.962 & 0.954 & 0.995 & 0.978 \\ \(su_{end}\) & 0.939 & 0.935 & 0.982 & 0.980 \\ \hline \hline \end{tabular}
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Table 4: Summary of training and testing R-square values for each proxy model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Proxy Model**} & \multicolumn{4}{c}{**Polynomial Regression**} & \multicolumn{4}{c}{**Neural Network**} \\ \cline{2-9}  & **Training MAE** & **Training RMSE** & **Testing MAE** & **Testing MAE** & **Training RMSE** & **Testing MAE** & **Testing RMSE** \\ \hline \(N_{p}\) (Mbbl) & 7.53 & 10.39 & 8.28 & 11.65 & 1.39 & 2.31 & 1.76 & 3.36 \\ \(q_{0 max}\) (bbl/d) & 221.6 & 281.5 & 239.9 & 303.6 & 63.4 & 97.6 & 74.3 & 126.4 \\ \(q_{end}\) (bbl/d) & 29.1 & 43.0 & 31.1 & 45.9 & 8.6 & 14.1 & 11.8 & 21.7 \\ \(p_{end}\) (psl) & 64.8 & 85.8 & 66.0 & 87.6 & 14.9 & 22.3 & 16.1 & 25.5 \\ \(T_{end}\) (F) & 2.5 & 3.8 & 2.6 & 4.2 & 0.9 & 1.4 & 1.3 & 2.9 \\ \(su_{end}\) & 0.0259 & 0.0331 & 0.0264 & 0.0338 & 0.0152 & 0.0208 & 0.0156 & 0.0218 \\ \hline \hline \end{tabular}
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Table 5: Summary of training and testing mean absolute error (MAE) and root mean square error (RMSE) for each proxy model. network model outperforms the polynomial regression model for the accuracy of all output predictions and lower MAE and RMSE values. Sobol analysis was conducted for each neural network model to determine the importance of each input parameter. Initial reservoir saturation and oil viscosity were found to be the parameters with the most contribution in computations of reservoir production performance parameters. In computations of reservoir parameters at the end of the injection cycle, the most significant parameters were the initial values of the output reservoir characterization parameters themselves. This research is focused on implementing a machine learning algorithm to build proxy models for one of the EOR methods, where the developed models can be utilized to assist users in designing simulation scenarios and to save a large amount of time. The workflow proposed in this study can be applied to create models with different production schemes for other unconventional production methods. The authors propose this research be expanded by introducing additional functionality to the existing model, such as the ability to account for various reservoir geometry configurations or injection of other enhancing fluids, such as chemicals, in steam huff and puff injection projects. Conceptualization, M.G.M. ; Methodology, M.G.M., S.R. and S.U.I. ; Software, M.G.M. and S.R. ; Validation, M.G.M., B.M.N. and S.U.I. ; Formal Analysis, M.G.M. and S.U.I. ; Investigation, M.G.M., B.M.N. and S.U.I. ; Resources, M.G.M. and S.R. ; Data Curation, M.G.M. ; Writing--Original Draft Preparation, M.G.M. ; Writing--Review and Editing, S.R., B.M.N. and S.U.I. ; Visualization, M.G.M., S.R. and S.U.I.