The Windowing Algorithm: Dimensionality Reduction in Grey-Box System Identification of Reservoir Network Models

The energy digitization requires development of fast and reliable computational models to simulate processes, seamlessly integrate signals from sensors, and actuate control systems for optimal returns and safe operation. In reservoir engineering, fast simulation of displacement processes in porous media is possible through material balance network models which connect injector and producer wells, and are known as capacitance resistance models. They have been applied to petroleum reservoirs undergoing water and CO2 injection, geothermal reservoirs, and carbon sequestration in aquifers. They are a linear dynamic systems approximation of the porous media flow phenomena, which only requires rate and pressure measurements for the identification of its dynamics. In this paper, an algorithmic formulation is presented for dimensionality reduction during systems identification which incorporates well locations and eliminates states and parameters related to distant injector-producer pairs. Two case studies exemplify the reduction in computational time and number of parameters estimated.