Oil-Rate Forecast by Inferring Fractional-Flow Models From Field Data With Koval Method Combined With the Capacitance/Resistance Model

Many empirical and analytical models were developed to forecast oil production. Empirical models (including data-driven models) can, for example, find correlations between oil cut and production, but they lack explicit knowledge of the physical behavior. Classic analytical models are loyal to reservoir physics. Nevertheless, they often require estimation of water saturation as a function of time, which is difficult to obtain for multiwell reservoirs. It is desirable to combine advantages of both empirical and analytical models and develop a physical-model-based method that uses field data to infer oil rate. In this paper, we propose to infer fractional-flow models from field data by use of the Koval (1963) theory. We inversely solved the Koval fractional-flow equation to obtain a relationship between water cut and dimensionless time. By history matching field water-cut data, two model parameters, the Koval factor and the producer-drainage volume, are estimated. Nevertheless, it is challenging to use the Koval approach as a predictive model directly because the injection contribution into each producer in a future-time horizon must be evaluated first. To address this issue, we combine the Koval approach with the capacitance/resistance model (CRM), which characterizes the injector/producer connectivities and response time. The material balance of fluids is established in a producer-based drainage volume to consider the contributions from nearby injectors and the time lag in production caused by reservoir/fluids compressibility. A regression approach is simultaneously advanced to minimize the model error. Because of robustly integrating the reservoir physical behavior and the data-driven approach, the combination of the Koval theory and the CRM can result in a synergy that leads to accurate oil-rate predictions. We validated this integrated method in synthetic homogeneous and heterogeneous reservoirs to test its reliability, and further applied it to a field case in western Venezuela. Case studies demonstrate that one can use this integrated model as a real-time tool to characterize interwell connection and to predict future oil production accurately.