# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 3 Results and Discussion
### Proxy Models for Predicting Reservoir Conditions after an Injection Cycle  
The reservoir condition outputs after one cycle are represented by reservoir pressure, reservoir temperature, and reservoir water saturation. These outputs address the reservoir parameters that are most likely to change in one injection cycle. The parameters are defined as the average parameter value in the reservoir model, assuming that the effect of steam injection has mostly diminished and a new injection cycle can be started in the reservoir. Predicted and simulated data points for each output are presented in Figures 11-16. Figure 11: Predicted and simulated plot of (**a**) training data and (**b**) testing data for reservoir pressure at the end of the cycle—polynomial regression model. Figure 12: Predicted and simulated plot of (**a**) training data and (**b**) testing data for reservoir pressure at the end of the cycle—neural network model. Figure 14: Predicted and simulated plot of (**a**) training data and (**b**) testing data for reservoir temperature at the end of the cycle—neural network model. Figure 13: Predicted and simulated plot of (**a**) training data and (**b**) testing data for reservoir temperature at the end of the cycle—polynomial regression model. The reservoir pressure values at the end of the injection cycle (\(p_{end}\)) from the results dataset range from 0 to 1200 psi. The polynomial model is the equation of the \(p_{end}\) output as a function of all input parameters. The neural network model of \(p_{end}\) has an architecture of three hidden layers with a 10-8-6 neuron configuration. For the training data, the R-square for the polynomial regression model and the neural network model is 0.878 and 0.991, while the R-square for the testing data is 0.877 and 0.989. The MAE of the training and testing data for the polynomial regression model is 64.8 psi and 66 psi and, for the neural network model, 14.9 psi and 16.1 psi. The RMSE of the training and testing data for the polynomial regression model is 85.8 psi and 87.6 psi and, for the neural network model, 22.3 psi and 25.5 psi. It can be seen in Figures 11 and 12 that the neural network model performs better than the polynomial regression model. The training and testing data in the neural network are generally clustered around the best fit curve. It is also worth highlighting that the neural network model predicted no negative values, in comparison to the polynomial regression model that yields some negative data points. The reservoir temperature values at the end of the injection cycle (\(T_{end}\)) from the results dataset range from 50 to 194 \({}^{\circ}\)F. The polynomial model is the equation of the \(T_{end}\) output as a function of all input parameters. The neural network model of \(T_{end}\) has an architecture of three hidden layers with an 8-6-4 neuron configuration. For training data, the R-square for the polynomial regression model and the neural network model is 0.962 and 0.995, while the R-square for the testing data is 0.954 and 0.978. The MAE of the training and testing data for the polynomial regression model is 2.5 \({}^{\circ}\)F and 2.6 \({}^{\circ}\)F and, for the neural network model, is 0.9 \({}^{\circ}\)F and 1.3 \({}^{\circ}\)F. The RMSE of the training and testing data for the polynomial regression model is 3.8 \({}^{\circ}\)F and 4.2 \({}^{\circ}\)F and, for the neural network model, is 1.4 \({}^{\circ}\)F and 2.9 \({}^{\circ}\)F. The performance between the two models does not differ much, though it can be seen that some training data points drift away in the prediction-simulation plot of the polynomial regression model. Overall, the training and testing data in the neural network fit well around the best fit curve. The reservoir water saturation values at the end of the injection cycle (\(sw_{end}\)) from the results dataset range from 0 to 0.88. The polynomial model is the equation of the \(sw_{end}\) output as a function of all input parameters.