Application of transfer functions to model water injection in hydrocarbon reservoir

Water flooding is one of the most economical methods to increase oil recovery. In order to improve the ultimate oil recovery during waterflooding, it is essential to provide an accurate forecast of reservoir performance. Hence, various methods have been utilized to simulate reservoirs. Although grid-based simulation is the most common and accurate method, time-consuming computation and the demand for large quantities of data restrict the use of this method. Sometimes, a quick overview of reservoir performance is sufficient or all required data are not accessible. Therefore, in this study a fast simulator is introduced to provide a quick overview with the minimum amount of data.A new method is presented to forecast the performance of water injection based on Transfer Function (TF). In this approach, it is assumed that a reservoir consists of a combination of TFs. The order and arrangement of TFs are chosen based on the physical conditions of the reservoir which are ascertained by examining several cases. The selected arrangement and orders can be extended to any other reservoirs. Injection and production rates act as input and output signals to these TFs, respectively. After analyzing input and output signals, the unknown parameters of TFs are calculated. Subsequently, it is possible to predict reservoir performance.Four different cases are employed to validate the derived equation. The results reveal a good agreement with those obtained from the common grid-based simulators. In addition, it has been demonstrated that the TF parameters depend on the characteristics and the pattern of different sections of the reservoir.This approach is a quick way to forecast waterflooding performance and can be a new window for the future of fast simulators. It provides the prediction with higher certainty in comparison with the other fast simulators. Furthermore, the only requirements for the method are injection and production rates. The analytical solution of the method enables its utilization in finding optimum rates for water injection in a short period of time. The method also presents some key parameters such as well connectivity. The use of the model is limited to situations when a rapid estimation is looked for and/or adequate data is not accessible.