# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 2 Methodology
### Predictive Model Development  
The CMG \(\text{CMOST}^{\text{TM}}\) module was utilized to develop the predictive model. This module was employed to run the generated simulation cases, record the output target results and alter the hyperparameters to build the predictive model. From 6304 simulation data, 80% of the result was treated as training data and the remaining 20% was treated as testing data. In this study, polynomial regression and artificial neural network models were developed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No** & **Parameter** & **Unit** & **Min** & **Max** \\ \hline
1 & Area & acre & 0.5 & 10 \\ \hline
2 & Net Thickness & ft & 20 & 100 \\ \hline
3 & Porosity & \% & 15 & 40 \\ \hline
4 & Permeability & mD & 250 & 2000 \\ \hline
5 & Kv/Kh Ratio & Fraction & 0.1 & 0.3 \\ \hline
6 & Oil Density & \({}^{\circ}\)API & 8 & 25 \\ \hline
7 & Andrade’s Viscosity Constant A & & 0.0001 & 0.001 \\ \hline
8 & Andrade’s Viscosity Constant B & & 3000 & 5750 \\ \hline
9 & Reservoir Temperature & F & 86 & 232 \\ \hline
10 & Reservoir Pressure & psia & 100 & 1000 \\ \hline
11 & Initial Water Saturation & Fraction & 0.2 & 0.6 \\ \hline
12 & Conate Water Saturation & Fraction & 0.125 & 0.4 \\ \hline
13 & Residual Oil Saturation (Oil–Water Table) & Fraction & 0.1 & 0.45 \\ \hline
14 & Critical Gas Saturation & Fraction & 0 & 0.1 \\ \hline
15 & Residual Oil Saturation (Liquid–Gas Table) & Fraction & 0.05 & 0.2 \\ \hline
16 & Kro at Conate Water Saturation & Fraction & 0.2 & 1 \\ \hline
17 & Kru at Irreducible Oil Saturation & Fraction & 0.2 & 1 \\ \hline
18 & Krg at Conate Liquid Saturation & Fraction & 0.2 & 1 \\ \hline
19 & Exponent for Krow & Fraction & 1 & 4 \\ \hline
20 & Exponent for Kruv & Fraction & 1 & 4 \\ \hline
21 & Exponent for Krog & Fraction & 1 & 4 \\ \hline
22 & Exponent for Krg & Fraction & 1 & 4 \\ \hline
23 & Steam Injection Rate & bbl/d & 200 & 1500 \\ \hline
24 & Steam Quality & Fraction & 0.6 & 0.95 \\ \hline
25 & Steam Temperature & \({}^{\circ}\)F & 250 & 500 \\ \hline
26 & Injection Period & days & 7 & 30 \\ \hline
27 & Soaking Period & days & 3 & 30 \\ \hline
28 & Production Period & days & 30 & 365 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input variables for sensitivity analysis and predictive model development. The polynomial regression (PR) method is a form of analysis to determine the relationship between input variables and response variables as a polynomial equation. The general quadratic polynomial regression is presented in Equation (6) below:  
\[y=a_{0}+\sum_{j=1}^{k}a_{j}x_{j}+\sum_{j=1}^{k}a_{jj}x_{j}^{2}+\sum_{i<1}\sum_{ j=1}^{k}a_{j}x_{j} \tag{6}\]  
where \(a_{0},\ a_{1},\dots,\ a_{k}\) are the coefficients of linear (\(x_{j}\)) terms, \(a_{jj}\) is the coefficient of quadratic (\(x_{j}^{2}\)) terms, and \(a_{ij}\) is the coefficient of the interaction (\(x_{i}x_{j}\)) terms. All coefficients are determined by using the least-squares method. It is common that some of the terms in the model are not statistically significant. The model can be improved by removing statistically insignificant terms, which can be determined by evaluating the significance probability. As the insignificant variables are reduced, the modified model is often named a reduced polynomial regression model. In this study, the reservoir performance outputs are represented as a reduced quadratic function of the 28 input parameters. Artificial neural network (ANN) is a model that emulates the biological neural system. It consists of nodes that are similar to neurons in the human brain. A node receives signals from adjacent nodes and processes them to produce an output. The ANN model structure is presented in Figure 4. It consists of an input layer, an output layer, and one or multiple hidden layers in between. Each neuron from a layer is connected to the neurons from other nearby layers with a connection called weight, which represents an influence of corresponding input on the connected neuron.