Summary
Several interwell connectivity models such as multiple linear regression (MLR) and the capacitance model (CM) have been proposed to model waterflooding performance in high-permeability reservoirs on the basis of observed production data. However, the existing methods are not effective at characterizing the behavior of transient flows that are prevalent in low-permeability reservoirs. This paper presents a novel dynamic waterflooding model that is based on linear dynamical systems (LDSs) to characterize the injection/production relationships in an oil field during both stationary and nonstationary production phases. We leverage a state-space model (SSM), in which the changing rates of control volumes between injector/producer pairs in the reservoir of interest serve as time-varying hidden states, depending on the reservoir condition. Thus, the model can better characterize the transient dynamics in low-permeability reservoirs. We propose a self-learning procedure for the model to train its parameters as well as the evolution of the hidden states only on the basis of past observations of injection and production rates. We tested the LDS method in comparison with the state-of-the-art CM method in a wide range of synthetic reservoir models including both high-permeability and low-permeability reservoirs, as well as various dynamic scenarios involving varying bottomhole pressure (BHP) of producers, injector shut-ins, and reservoirs of larger scales. We also tested LDS on the real production data collected from Changqing oil field containing low-permeability formations. Testing results demonstrate that an LDS significantly outperforms CM in terms of modeling and predicting waterflooding performance in low-permeability reservoirs and various dynamic scenarios.
