A MULTIVARIATE AUTOREGRESSIVE MODEL FOR CHARACTERIZING PRODUCER PRODUCER RELATIONSHIPS IN WATERFLOODS FROM INJECTION/PRODUCTION RATE FLUCTUATIONS

Recently, a new research trend has focused on building reliable signal processing models to characterize communications among wells in waterfloods, using only injection/production data. Among these we can cite Capacitance Model (CM) descried by Yousef et al. (SPE95322) and our previous work: finite‑impulse‑response (FIR) model (SPE121353). In these approaches, the producers are often assumed to be independent of each other and to be only influenced by nearby injectors. We present an improved approach based on a multivariate autoregressive model with extra‑inputs (M‑ARX), which models the interaction among all injectors and producers (including producer to producer interactions) in a region‑of‑interest (ROI), using a set of linear differential/difference equations and solved by quadratic programming techniques. By coupling all injection/production rates in the ROI, the ARX model outperforms other models in terms of prediction, while keeping the number of unknown parameters relatively small compared to the FIR model. More importantly, when the rates of some producers change significantly, e.g., shutting‑in of a producer, the ARX model does not have to be modified to handle the changes, while other models need to be re‑trained. Our evaluation, under various scenarios using bench type simulated performance data, shows that under similar number of parameters, the ARX model outperforms CM in terms of prediction ability (within average of 65% lower prediction‑error). We also show a case study for a waterflood case in California to demonstrate the superiority of the ARX model. Compared to the Compensated Capacitance Model (CCM) by Kaviani et al. (SPE117856), which also captures producer‑producer relationships, our approach is more general because the ARX model allows coupling all rate information available (injection/production rates) in the ROI, but CCM can only handle the special case of shutting in a producer.