# Reservoir Performance Prediction in Steam Huff and Puff Injection Using Proxy Modelling
## 1 Introduction  
The maturity of most giant oil fields motivates the utilization of unconventional recovery methods to increase oil production [1]. After the primary and secondary recovery stages, enhanced oil recovery (EOR) has the potential to enable the recovery of a significant amount of oil that remains in the reservoir. EOR involves the injection of a fluid or fluids into the reservoir to supply the energy required for oil displacement. Furthermore, the injected fluids interact with the reservoir rock and formation fluid, which results in altering the physical properties of the rock and creating advantageous conditions for oil recovery [2, 3, 4]. One of the main EOR methods applied worldwide is thermal EOR. This method supported more than 40% of total EOR production in 2015 [5]. The mechanism of the thermal EOR method is based on reducing oil viscosity at an increased reservoir temperature. This implies that the target oil is a high-density and high-viscosity oil. Heavy oils are such an example for the target oil, and several reports on thermal EOR implementations showed that almost all of the reservoirs are heavy oil reservoirs [6, 7, 8]. Steam huff and puff injection, also known as cyclic steam stimulation, is the method comprising cyclical steam injection into a well. After injection, the well is shut in to allow the steam to \"soak\" into the reservoir. The high temperature of the steam should reduce oil viscosity near the steam-oil interface. This period is called the soaking period. The well is opened again after the soaking period, producing oil at a higher rate. During the soaking period, most of the steam is condensed so the well produces both hot oil and hot water. This increase in well production performance happens because of the reduction in oil viscosity and the increase in reservoir pressure near the wellbore. After some time, the heat dissipates and oil viscosity increases. After the production declines to the pre-defined level, steam is reinjected into the well, starting a new injection/production cycle. This whole process of injection, soaking, and production is called the huff and puff method. Steam huff and puff injection is one of the most used thermal EOR methods due to its economical attractiveness and effectiveness. Furthermore, it is often used as a precursor before conducting a full field-scale steam injection. Successes in previous developed experience of this method were reported in Cold Lake Field, Canada [9; 10], Midway Sunset Field, California [11], Duri Field, Indonesia [12; 13; 14] and Tia Juana Field, Venezuela [15; 16]. In Cold Lake Field, a 100,000 cp bitumen was found and 20% of the reserves was recovered by implementing this method. In Midway Sunset Field, more than 19,000 steam cycles were performed in 1500 wells over a period of 23 years. In Duri Field, the oil production rate was increased by almost five-fold and steam huff and puff injection became a precursor to a steamflood pilot, which led to the largest steamflood implementation in the world. In Tia Juana Field, the method was applied to 145 wells and produced 30.7 million barrels of oil in 7 years. Reservoir simulation is a crucial tool in reservoir engineering. It allows the simulation of the behavior of a dynamic reservoir model in response to the disturbance caused by the production operation. Moreover, it has become a standard in evaluating the performance of a reservoir and designing an optimized production scheme. However, despite the progress in computational hardware, the whole process of reservoir simulation remains time-consuming and expensive due to the high non-linearity of a reservoir system and the difficulty of building a reliable full reservoir model. The cost and time inefficiency problem of reservoir simulation persists in designing a production scheme for steam huff and puff injection. Building predictive proxy models is a suitable solution to deal with this issue. A proxy model is a mathematically or statistically defined function that represents a real system or its simulation [17].