# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 3 Results and Discussion
### Evaluation of Model Fitting and Performance Metrics  
A summary of evaluation metrics for each proxy model is presented in Tables 4 and 5. It can be seen that, in general, the performance of the neural network models is optimum compared to the polynomial regression models. This is due to the nature of both models, where the high nonlinearity presented in this modeling problem is well captured by the neural network model compared to the polynomial regression model. For training and testing data of the neural network model, almost all of the R-square values are above 0.9, which shows a good fit. Additionally, the MAE and RMSE values are notably lower than the polynomial models. A good agreement between the fitting indicator of training and testing data indicates that the model is not overfitting. Overfitting in a model is undesirable, as that implies that the model only remembers the training data and may perform poorly when exposed to unseen test data. This is considered when designing the experiment cases, where the combination of input parameter values is unique for each case.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Proxy Model**} \\ \hline \multicolumn{2}{c}{\(P_{end}\)} & \multicolumn{2}{c}{\(T_{end}\)} & \multicolumn{2}{c}{\(sw_{end}\)} \\ \hline
**Input** & **Contribution (\%)** & **Input** & **Contribution (\%)** & **Input** & **Contribution (\%)** \\ \hline Pressure & 32.7 & Temperature & 50.9 & Sw & 78.5 \\ Sw & 24.5 & Area & 3.3 & Pressure & 3.4 \\ ViscB & 15.5 & Thickness & 2.5 & Swcon & 2.8 \\ Area & 8.3 & InjRate & 2.5 & Area & 1.4 \\ ProductionPeriod & 8.2 & Sw & 2.2 & NW & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Input parameters with the highest contribution towards the output for each proxy model of reservoir conditions after an injection cycle based on Sobol analysis.  
The observations from the prediction and simulated plot demonstrate that deviations in testing data points are seen past a certain threshold for each neural network model--for instance, above 20 Mbbl values in the testing data for the \(N_{p}\) model. As mentioned previously, any deviation past this value may occur as a result of the imbalanced proportion of data points along the output interval. After running the simulation, the cumulative oil production data below 20 Mbbl are around 90% of the results. This leads to fewer data being provided into the model above that threshold, affecting the model's accuracy. The same can be expressed for the \(q_{end}\) model, where the testing data points drift significantly past the 20 bbl/day threshold, resulting in a relatively lower R-square value in comparison to the other neural network models. Inversely, it can be inferred that the prediction performance for results below that threshold is excellent. For this specific model, possible improvement can be applied through creating separate proxy models for low and high values of \(q_{end}\) based on that threshold, which will include re-evaluating input values and their distributions that result in low and high \(q_{end}\) predictions.  
The neural network models presented in this study can be applied for accurately determining reservoir performance in steam huff and puff injection. These predictive models save a large amount of time and costs and are believed to be helpful in assisting users for designing simulation scenarios. It is worth noting the limitation of the proxy model that it is only applicable as long as the input parameter values are within the parameter intervals of the model. The workflow used in this study can be applied for developing proxy models of other reservoir configurations or injection method variations; for example, in a fractured reservoir or a chemical-assisted steam huff and puff injection.