# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 2 Methodology
### Synthetic Reservoir Model  
The reservoir model was developed based on the SPE 4 th comparative study [43], as illustrated in Figure 2. It is a cylindrical grid model with 20 radial grids, 1 angular grid, and 4 vertical grids. As the huff and puff method incorporates injection, soaking and production in one well, a cylindrical geometry is preferred due to its advantage in representing the radially dominated flow around a single wellbore. The radial grid around a near-well area is refined to capture the thermal mechanism and fluid flow around the wellbore better. It has 1 well positioned at the center, which serves as both an injector and producer. All grids of the well are perforated, and reservoir properties are homogeneous for every grid. Figure 1: The overall flowchart methodology of proxy model development for steam huff and puff injection in this study. Oil viscosity is considered as an input parameter for this model. The oil viscosity vs. temperature table was generated using [PERSON]'s correlation as shown in Equation (1) [44]. Relative permeability functions were built using [PERSON]'s equation, presented via Equation (2) to Equation (5) [45]. The oil-water system was covered by Equations (2) and (3) and the gas-liquid system was covered by Equations (4) and (5). The variation in Corey exponents (\(n_{o},n_{ow},n_{og},n_{g}\)) covered both sandstone and carbonate rock types. \[\mu_{o}=A\times e^{\frac{\beta}{T}} \tag{1}\]  
\[k_{row}=k_{rocw}\bigg{[}\frac{1-S_{w}-S_{orw}}{1-S_{wc}-S_{orw}}\bigg{]}^{n_{o}} \tag{2}\]  
\[k_{rw}=k_{reiruo}\bigg{[}\frac{S_{w}-S_{wc}}{1-S_{wc}-S_{orw}}\bigg{]}^{n_{ow}} \tag{3}\]  
\[k_{rog}=k_{rogcg}\bigg{[}\frac{1-S_{g}-S_{lc}}{1-S_{gc}-S_{lc}}\bigg{]}^{n_{cg}} \tag{4}\]  
\[k_{rg}=k_{rgcd}\bigg{[}\frac{S_{g}-S_{gc}}{1-S_{lc}-S_{gc}}\bigg{]}^{n_{g}} \tag{5}\]  
In Equation (1), \(\mu_{o}\) is the oil viscosity, \(A\) and \(B\) are the Andrade viscosity constants, and \(T\) is the temperature in \({}^{\circ}\)F. For the oil-water relative permeability system in Equations (2) and (3), \(k_{row}\) is the oil relative permeability and \(k_{rw}\) is the water relative permeability. \(k_{rocw}\) is the oil relative permeability at connate water saturation \((S_{av})\); \(k_{ruiro}\) is the water relative permeability at irreducible oil saturation \((S_{orw})\). \(n_{o}\) is the [PERSON] exponent for \(k_{row}\) and \(n_{ow}\) is the [PERSON] exponent for \(k_{rw}\). For the gas-liquid relative permeability system in Equations (4) and (5), \(k_{rog}\) is the liquid relative permeability and \(k_{rg}\) is the gas relative permeability. \(k_{rogcg}\) is the liquid relative permeability at connate gas saturation \(\big{(}S_{gc}\big{)}\) and \(k_{rgcl}\) is the gas relative permeability at connate liquid saturation \((S_{lc})\). \(n_{og}\) is the [PERSON] exponent for \(k_{rog}\) and \(n_{g}\) is the [PERSON] exponent for \(k_{rg}\). The operating parameters are steam injection rate, steam quality, steam temperature, soaking period, injection period, and production period. The initial condition of the reservoir is adjusted to be within the range of reservoir conditions of the screening criteria for steam huff and puff. Steam, with varying quality and temperature, is the injected fluid. The model simulates an injection scheme for one cycle, consisting of injection, soaking,  
Figure 2: Synthetic 1-well, 3D cylindrical reservoir model. and production periods. This thermal reservoir model is simulated using the commercial simulator CMG STARSTM. The 3D model was then validated by comparing the results of oil production history from this model with actual field data, where the field parameters and results used are from the Midway Sunset field [46]. Figure 3 shows the history matching of oil production rate from this simulation model to the field data, which expressed good agreement. Furthermore, the cumulative oil production result from this model is 878 m\({}^{3}\), in comparison to field data, which is 888 m\({}^{3}\). This suggests that they are in good agreement with each other.