Subspace identification of low-order reservoir models

We present a novel approach to identify low-order models of heterogeneous reservoirs. The identification is based on flowrate-pressure input-output behavior (interference tests) and order reduction using subspace system identification. We generated synthetic data with a simple finite difference model of single-phase flow in a two-dimensional reservoir (confined aquifer) to investigate the scope of the method. The reservoir contained a row of injection wells at one side and a row of production wells at the opposite side. The input for the identification process consisted of random time sequences of step functions in the flow rate at both the injectors and the producers. The output consisted of pressure measurements in the same wells. In several examples, one of which is presented in the paper, it proved possible to successfully identify low order reservoir models, at least for the synthetic data used. The pressure response of the identified models to random input sequences closely resembled the response of the original models. In the example presented, the original, data generating, model was successfully identified and the verification error remained rather low, even when only 24 'most dominant modes' (states) of the full order (64) identified model were used.