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

Abstract

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.

Ensemble-based optimization of interwell connectivity in heterogeneous waterflooding reservoirs

“…Moreover, the Koval water fractional-flow equation developed by Cao et al (2014Cao et al ( , 2015 is applied to separate the oil production from total production. Thereafter, a novel ensemble-based optimization framework preconditioning hybrid nonlinear constraints is then provided to minimize the squared difference between the predicted and observed production data, so that the interwell geological parameters such as connectivity coefficients, time constants, and drained pore volumes will be eventually estimated.…”

“…By history matching field water cut data, two characteristic parameters, the Koval factor and drainage volume, are estimated, which takes the form of Eq. (8) (Cao et al, 2014(Cao et al, , 2015.…”

“…Nevertheless, the Buckley-Leverett model has many assumptions such as homogenous media, one dimension flow, incompressible system, negligible gravity and capillarity, all of which should be carefully understood prior to application. Cao et al (2014Cao et al ( , 2015 provide a water fractional flow equation inferred from field production data using the Koval theory. By history matching field water cut data, two model parameter, Koval factor and drained pore volume, will be estimated.…”

Improved CRM Model for Inter-Well Connectivity Estimation and Production Optimization: Case Study for Karst Reservoirs

“…Holanda et al [19] further introduced the state-space (SS) theory to describe the dynamic behavior of CRMs as a multi-input/multi-output system. Capacitance-resistance models were also incorporated with fractional flow models [20,21] to allow the prediction of oil rates. It indicated that the Koval model proposed by Cao et al [21] may not be a good choice for mature waterfloods, but it is effective enough to revisit abrupt breakthroughs caused by active aquifer support, which widely exist in karst carbonate reservoirs.…”

“…Capacitance-resistance models were also incorporated with fractional flow models [20,21] to allow the prediction of oil rates. It indicated that the Koval model proposed by Cao et al [21] may not be a good choice for mature waterfloods, but it is effective enough to revisit abrupt breakthroughs caused by active aquifer support, which widely exist in karst carbonate reservoirs. During production of karst reservoirs, large-scale fractured-vuggy units are usually treated as isolated targets for continuous waterflood, thereby the previous CRM models should be modified to supply the aquifer influx rate as needed with all contributing injection rates.Owing to the fact that understanding reservoir fluid dynamics to achieve optimal decision-making by grid-based reservoir models is computationally expensive and frequently require large volumes of uncertain data to estimate petrophysical properties, full field-scale models are not easy for rapid reservoir analysis to make reliable decisions.…”